Journal articles: 'Mapping (Mathematics) Topological spaces'

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Noll, Dominik. "Open mapping theorems in topological spaces." Czechoslovak Mathematical Journal 35, no. 3 (1985): 373–84. http://dx.doi.org/10.21136/cmj.1985.102027.

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Ramadan, A. A., S. E. Abbas, and A. A. Abd El-Latif. "Compactness in intuitionistic fuzzy topological spaces." International Journal of Mathematics and Mathematical Sciences 2005, no. 1 (2005): 19–32. http://dx.doi.org/10.1155/ijmms.2005.19.

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We introduce fuzzy almost continuous mapping, fuzzy weakly continuous mapping, fuzzy compactness, fuzzy almost compactness, and fuzzy near compactness in intuitionistic fuzzy topological space in view of the definition of Šostak, and study some of their properties. Also, we investigate the behavior of fuzzy compactness under several types of fuzzy continuous mappings.

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Gunduz (Aras), Cigdem, and Sadi Bayramov. "Some Results on Fuzzy Soft Topological Spaces." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/835308.

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We introduce some important properties of fuzzy soft topological spaces. Furthermore, fuzzy soft continuous mapping, fuzzy soft open and fuzzy soft closed mappings, and fuzzy soft homeomorphism for fuzzy soft topological spaces are given and structural characteristics are discussed and studied.

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Xu, Zhen-Guo, and Fu-Gui Shi. "Some weakly mappings on intuitionistic fuzzy topological spaces." Tamkang Journal of Mathematics 39, no. 1 (March 31, 2008): 25–32. http://dx.doi.org/10.5556/j.tkjm.39.2008.42.

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In this paper, we shall introduce concepts of fuzzy semiopen set, fuzzy semiclosed set, fuzzy semiinterior, fuzzy semiclosure on intuitionistic fuzzy topological space and fuzzy open (fuzzy closed) mapping, fuzzy irresolute mapping, fuzzy irresolute open (closed) mapping, fuzzy semicontinuous mapping and fuzzy semiopen (semiclosed) mapping between two intuitionistic fuzzy topological spaces. Moreover, we shall discuss their some properties.

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Liu, Xin, and Shou Lin. "On spaces defined by Pytkeev networks." Filomat 32, no. 17 (2018): 6115–29. http://dx.doi.org/10.2298/fil1817115l.

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The notions of networks and k-networks for topological spaces have played an important role in general topology. Pytkeev networks, strict Pytkeev networks and cn-networks for topological spaces are defined by T. Banakh, and S. Gabriyelyan and J. K?kol, respectively. In this paper, we discuss the relationship among certain Pytkeev networks, strict Pytkeev networks, cn-networks and k-networks in a topological space, and detect their operational properties. It is proved that every point-countable Pytkeev network for a topological space is a quasi-k-network, and every topological space with a point-countable cn-network is a meta-Lindel?f D-space, which give an affirmative answer to the following problem [25, 29]: Is every Fr?chet-Urysohn space with a pointcountable cs'-network a meta-Lindel?f space? Some mapping theorems on the spaces with certain Pytkeev networks are established and it is showed that (strict) Pytkeev networks are preserved by closed mappings and finite-to-one pseudo-open mappings, and cn-networks are preserved by pseudo-open mappings, in particular, spaces with a point-countable Pytkeev network are preserved by closed mappings.

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MA, TSOY-WO. "INVERSE MAPPING THEOREM ON COORDINATE SPACES." Bulletin of the London Mathematical Society 33, no. 4 (July 2001): 473–82. http://dx.doi.org/10.1017/s0024609301008050.

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A mean-value theorem, an inverse mapping theorem and an implicit mapping theorem are established here in a class of complex locally convex spaces, including the spaces of test functions in distribution theory. Our main tool is the integral formula and the invariance of the domain, derived from topological degrees, rather than from fixed points of contractions in Banach spaces.

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Singh Rajput, Alpa, S. S. Thakur, and Om Prakash Dubey. "SOFT ALMOST β-CONTINUITY IN SOFT TOPOLOGICAL SPACES." International Journal of Students' Research in Technology & Management 8, no. 2 (June 16, 2020): 06–14. http://dx.doi.org/10.18510/ijsrtm.2020.822.

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Purpose: In the present paper the concept of soft almost β-continuous mappings and soft almost β-open mappings in soft topological spaces have been introduced and studied. Methodology: This notion is weaker than both soft almost pre-continuous mappings, soft almost semi-continuous mapping. The diagrams of implication among these soft classes of soft mappings have been established. Main Findings: We extend the concept of almost β-continuous mappings and almost β-open mappings in soft topology. Implications: Mapping is an important and major area of topology and it can give many relationships between other scientific areas and mathematical models. This notion captures the idea of hanging-togetherness of image elements in an object by assigning strength of connectedness to every possible path between every possible pair of image elements. It is an important tool for the designing of algorithms for image segmentation. The novelty of Study: Hope that the concepts and results established in this paper will help the researcher to enhance and promote the further study on soft topology to carry out a general framework for the development of information systems.

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Dineen, Seán, Pablo Galindo, Domingo García, and Manuel Maestre. "Linearization of holomorphic mappings on fully nuclear spaces with a basis." Glasgow Mathematical Journal 36, no. 2 (May 1994): 201–8. http://dx.doi.org/10.1017/s0017089500030743.

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In [13] Mazet proved the following result.If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].

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Das, Birojit, Baby Bhattacharya, and Apu Kumar Saha. "Some remarks on fuzzy infi topological spaces." Proyecciones (Antofagasta) 40, no. 2 (April 2021): 399–415. http://dx.doi.org/10.22199/issn.0717-6279-2021-02-0024.

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Induced fuzzy infi topological space is already introduced by Saha and Bhattacharya [Saha A.K., Bhattacharya D. 2015, Normal Induced Fuzzy Topological Spaces, Italian Journal of Pure and Applied Mathematics, 34, 45-56]. In this paper for the said space, we further analyse some properties viz. fuzzy I-continuity, fuzzy infi open mappings and fuzzy infi closed mappings etc. Also we study product fuzzy infi topological space and establish some results concerned with it.

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Borsík, Ján, Lubica Holá, and Dusan Holý. "Baire spaces and quasicontinuous mappings." Filomat 25, no. 3 (2011): 69–83. http://dx.doi.org/10.2298/fil1103069b.

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The notion of quasicontinuity was perhaps the first time used by R. Baire in [2]. Let X, Y be topological spaces and Q(X,Y) be the space of quasicontinuous mappings from X to Y. If X is a Baire space and Y is metrizable, in Q(X,Y) we can approach each (x, y) in the graph Grf of f along some trajectory of the form {(xk, fnk (xk )): k??} if and only if we can approach most points along a vertical trajectory. This result generalizes Theorem 5 from [3]. Moreover in the class of topological spaces with the property QP we give a characterization of Baire spaces by the above mentioned fact. We also study topological spaces with the property QP.

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Çetkin, Vildan. "Gradation of Continuity for Fuzzy Soft Mappings." Journal of Mathematics 2021 (August 19, 2021): 1–12. http://dx.doi.org/10.1155/2021/2691753.

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This paper is devoted to describe the notion of a parameterized degree of continuity for mappings between L -fuzzy soft topological spaces, where L is a complete De Morgan algebra. The degrees of openness, closedness, and being a homeomorphism for the fuzzy soft mappings are also presented. The properties and characterizations of the proposed notions are pictured. Besides, the degree of continuity for a fuzzy soft mapping is unified with the degree of compactness and connectedness in a natural way.

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Sullivan, R. P., and J. H. Rubinstein. "Continuous nilpotents on topological spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 1 (August 1987): 127–36. http://dx.doi.org/10.1017/s1446788700039501.

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AbstractK. D. Magill has investigated the semigroup generated by the idempotent continuous mappings of a topological space into itself and examined whether this semigroup determines the space to within homeomorphism. By analogy with this (and related work of Bridget Bos Baird) we now consider the semigroup generated by nilpotent continuous partial mappings of a space into itself.

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WANG, HANFENG, WEI HE, and JING ZHANG. "ON -UNFAVOURABLE SPACES." Bulletin of the Australian Mathematical Society 102, no. 3 (March 16, 2020): 439–50. http://dx.doi.org/10.1017/s0004972720000192.

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To study when a paratopological group becomes a topological group, Arhangel’skii et al. [‘Topological games and topologies on groups’, Math. Maced. 8 (2010), 1–19] introduced the class of $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$-unfavourable spaces. We show that every $\unicode[STIX]{x1D707}$-complete (or normal) $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$-unfavourable semitopological group is a topological group. We prove that the product of a $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$-unfavourable space and a strongly Fréchet $(\unicode[STIX]{x1D6FC},G_{\unicode[STIX]{x1D6F1}})$-favourable space is $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$-unfavourable. We also show that continuous closed irreducible mappings preserve the $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$-unfavourableness in both directions.

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FRAJZADEH, ALI P., and MUHAMMAD ASLAM NOOR. "GENERALIZED MIXED QUASI-COMPLEMENTARITY PROBLEMS IN TOPOLOGICAL VECTOR SPACES." ANZIAM Journal 49, no. 4 (April 2008): 525–31. http://dx.doi.org/10.1017/s1446181108000084.

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AbstractIn this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping theorem, we study the existence of a solution of the generalized mixed quasi-variational inequalities and generalized mixed quasi-complementarity problems. Several special cases are also discussed. The results obtained in this paper can be viewed as extension and generalization of the previously known results.

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Majeed, Rasha Naser. "C̆ech Fuzzy Soft Closure Spaces." International Journal of Fuzzy System Applications 7, no. 2 (April 2018): 62–74. http://dx.doi.org/10.4018/ijfsa.2018040103.

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In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

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Diegmiller, Rocky, Lun Zhang, Marcio Gameiro, Justinn Barr, Jasmin Imran Alsous, Paul Schedl, Stanislav Y. Shvartsman, and Konstantin Mischaikow. "Mapping parameter spaces of biological switches." PLOS Computational Biology 17, no. 2 (February 8, 2021): e1008711. http://dx.doi.org/10.1371/journal.pcbi.1008711.

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Since the seminal 1961 paper of Monod and Jacob, mathematical models of biomolecular circuits have guided our understanding of cell regulation. Model-based exploration of the functional capabilities of any given circuit requires systematic mapping of multidimensional spaces of model parameters. Despite significant advances in computational dynamical systems approaches, this analysis remains a nontrivial task. Here, we use a nonlinear system of ordinary differential equations to model oocyte selection inDrosophila, a robust symmetry-breaking event that relies on autoregulatory localization of oocyte-specification factors. By applying an algorithmic approach that implements symbolic computation and topological methods, we enumerate all phase portraits of stable steady states in the limit when nonlinear regulatory interactions become discrete switches. Leveraging this initial exact partitioning and further using numerical exploration, we locate parameter regions that are dense in purely asymmetric steady states when the nonlinearities are not infinitely sharp, enabling systematic identification of parameter regions that correspond to robust oocyte selection. This framework can be generalized to map the full parameter spaces in a broad class of models involving biological switches.

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Murtaza, Ghulam, Mujahid Abbas, and Muhammad Ali. "Fixed points of interval valued neutrosophic soft mappings." Filomat 33, no. 2 (2019): 463–74. http://dx.doi.org/10.2298/fil1902463m.

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In this paper, we introduce some new notions such as interval valued neutrosophic soft points, interval valued neutrosophic soft mappings, interval valued neutrosophic soft Hausdorff topological spaces, and interval valued neutrosophic soft compact topological spaces. Cantor?s intersection theorem is proved for interval valued neutrosophic soft sets. The aim of this paper is to establish the existence of fixed points of interval valued neutrosophic soft mappings on interval valued neutrosophic soft compact topological spaces. Some examples are provided to support the concepts and the results presented herein.

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Banakh, T. O., V. I. Bogachev, and A. V. Kolesnikov. "Topological Spaces with the Strong Skorokhod Property." gmj 8, no. 2 (June 2001): 201–20. http://dx.doi.org/10.1515/gmj.2001.201.

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Abstract We study topological spaces with the strong Skorokhod property, i.e., spaces on which all Radon probability measures can be simultaneously represented as images of Lebesgue measure on the unit interval under certain Borel mappings so that weakly convergent sequences of measures correspond to almost everywhere convergent sequences of mappings. We construct nonmetrizable spaces with such a property and investigate the relations between the Skorokhod and Prokhorov properties. It is also shown that a dyadic compact has the strong Skorokhod property precisely when it is metrizable.

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Ruiz, L. M. Sánchez. "On some topological vector spaces related to the general open mapping theorem." Acta Mathematica Hungarica 61, no. 3-4 (September 1993): 235–40. http://dx.doi.org/10.1007/bf01874683.

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Kordek, Kevin. "Picard Groups of Moduli Spaces of Curves with Symmetry." International Mathematics Research Notices 2020, no. 23 (October 31, 2018): 9293–335. http://dx.doi.org/10.1093/imrn/rny247.

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Abstract We study the Picard groups of moduli spaces of smooth complex projective curves that have a group of automorphisms with a prescribed topological action. One of our main tools is the theory of symmetric mapping class groups. In the 1st part of the paper, we show that, under mild restrictions, the moduli spaces of smooth curves with an abelian group of automorphisms of a fixed topological type have finitely generated Picard groups. In certain special cases, we are able to compute them exactly. In the 2nd part of the paper, we show that finite abelian level covers of the hyperelliptic locus in the moduli space of smooth curves have finitely generated Picard groups. We also compute the Picard groups of the moduli spaces of hyperelliptic curves of compact type.

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Zabeti, Omid, and Ljubisa Kocinac. "A few remarks on bounded operators on topological vector spaces." Filomat 30, no. 3 (2016): 763–72. http://dx.doi.org/10.2298/fil1603763z.

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We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators. We also consider similar types of bounded bilinear mappings between topological vector spaces. Some properties of tensor product operators between locally convex spaces are established. In the last part of the paper we deal with operators on topological Riesz spaces.

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M. Al-shami, Tareq. "Homeomorphism and Quotient Mappings in Infrasoft Topological Spaces." Journal of Mathematics 2021 (August 10, 2021): 1–10. http://dx.doi.org/10.1155/2021/3388288.

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In this paper, we contribute to infrasoft topology which is one of the recent generalizations of soft topology. Firstly, we redefine the concept of soft mappings to be convenient for studying the topological concepts and notions in different soft structures. Then, we introduce the concepts of open, closed, and homeomorphism mappings in the content of infrasoft topology. We establish main properties and investigate the transmission of these concepts between infrasoft topology and its parametric infratopologies. Finally, we define a quotient infrasoft topology and infrasoft quotient mappings and study their main properties with the aid of illustrative examples.

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El-Shafei, M. E., and A. H. Zakari. "Wθg-Closed andWδg-Closed in[0,1]-Topological Spaces." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/853870.

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We investigate various classes of generalized closed fuzzy sets in[0,1]-topological spaces, namely,Wθg-closed fuzzy sets andWδg-closed fuzzy sets. Also, we introduce a new separation axiomFT3/4∗of the[0,1]-topological spaces, and we prove that everyFT3/4∗-space is aFT3/4-space. Furthermore, we using the new generalized closed fuzzy sets to construct new types of fuzzy mappings.

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Al, Ghour, and Bayan Irshedat. "The topology of θω-open sets." Filomat 31, no. 16 (2017): 5369–77. http://dx.doi.org/10.2298/fil1716369a.

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We define the ??-closure operator as a new topological operator. We show that ??-closure of a subset of a topological space is strictly between its usual closure and its ?-closure. Moreover, we give several sufficient conditions for the equivalence between ??-closure and usual closure operators, and between ??-closure and ?-closure operators. Also, we use the ??-closure operator to introduce ??-open sets as a new class of sets and we prove that this class of sets lies strictly between the class of open sets and the class of ?-open sets. We investigate ??-open sets, in particular, we obtain a product theorem and several mapping theorems. Moreover, we introduce ?-T2 as a new separation axiom by utilizing ?-open sets, we prove that the class of !-T2 is strictly between the class of T2 topological spaces and the class of T1 topological spaces. We study relationship between ?-T2 and ?-regularity. As main results of this paper, we give a characterization of ?-T2 via ??-closure and we give characterizations of ?-regularity via ??-closure and via ??-open sets.

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Sarsak, Mohammad S. "On Semicompact Sets and Associated Properties." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–8. http://dx.doi.org/10.1155/2009/465387.

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We continue the study of semicompact sets in a topological space. Several properties, mapping properties of semicompact sets are studied. A special interest to spaces is given, where a space is if every subset of which is semicompact in is semiclosed; we study several properties of such spaces, it is mainly shown that a semi- semicompact space is if and only if it is extremally disconnected. It is also shown that in an -regular space if every point has an neighborhood, then is .

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Shah, Masood, Nawab Hussain, and Ljubomir Ciric. "Existence of fixed points of mappings on general topological spaces." Filomat 28, no. 6 (2014): 1237–46. http://dx.doi.org/10.2298/fil1406237s.

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The existence of fixed points for continuous mappings on general topological spaces via compact subsets is proved. All our results presented here are new and are generalizations, extensions and improvements of the corresponding results due to Ciric, Jungck, Liu and many others. Further, certain results due to Ciric are improved and extended to topological spaces which are not necessarily Hausdorff and completely regular.

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Alsharari, Fahad. "£-Single Valued Extremally Disconnected Ideal Neutrosophic Topological Spaces." Symmetry 13, no. 1 (December 31, 2020): 53. http://dx.doi.org/10.3390/sym13010053.

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This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-Ri (r-SVNIRi, for short), where i={0,1,2,3}, and r-single valued neutrosophic ideal-Tj (r-SVNITj, for short), where j={1,2,212,3,4}, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied.

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Magill, K. D. "Monomorphisms of Semigroups of Local Dendrites." Canadian Journal of Mathematics 38, no. 4 (August 1, 1986): 769–80. http://dx.doi.org/10.4153/cjm-1986-040-2.

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When we speak of the semigroup of a topological space X, we mean S(X) the semigroup of all continuous self maps of X. Let h be a homeomorphism from a topological space X onto a topological space Y. It is immediate that the mapping which sends f ∊ S(X) into h º f º h−1 is an isomorphism from the semigroup of X onto the semigroup of Y. More generally, let h be a continuous function from X into Y and k a continuous function from Y into X such that k º h is the identity map on X. One easily verifies that the mapping which sends f into h º f º k is a monomorphism from S(X) into S(Y). Now for “most” spaces X and Y, every isomorphism from S(X) onto S(Y) is induced by a homeomorphism from X onto Y. Indeed, a number of the early papers dealing with S(X) were devoted to establishing this fact.

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GAO, YIN-ZHU, and WEI-XUE SHI. "A NOTE ON PARACOMPACT p-SPACES AND THE MONOTONE D-PROPERTY." Bulletin of the Australian Mathematical Society 83, no. 3 (February 7, 2011): 463–69. http://dx.doi.org/10.1017/s0004972710001991.

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AbstractFor any generalized ordered space X with the underlying linearly ordered topological space Xu, let X* be the minimal closed linearly ordered extension of X and $\tilde {X}$ be the minimal dense linearly ordered extension of X. The following results are obtained. (1)The projection mapping π:X*→X, π(〈x,i〉)=x, is closed.(2)The projection mapping $\phi : \tilde {X} \rightarrow X_u$, ϕ(〈x,i〉)=x, is closed.(3)X* is a monotone D-space if and only if X is a monotone D-space.(4)$\tilde {X}$ is a monotone D-space if and only if Xu is a monotone D-space.(5)For the Michael line M, $\tilde {M}$ is a paracompact p-space, but not continuously Urysohn.

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Lin, Shou, and Ying Ge. "Preservations of so-metrizable spaces." Filomat 26, no. 4 (2012): 801–7. http://dx.doi.org/10.2298/fil1204801l.

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A space is called an so-metrizable space if it is a regular space with a ?-locally finite sequentially open network. This paper proves that so-metrizable spaces are preserved under perfect mappings and under closed sequence-covering mappings, which give an affirmative answer to a question on preservations of so-metrizable spaces under some closed mappings. Also, we prove that the closed image of an so-metrizable space is an so-metrizable space if it is a topological group.

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Sarsak, Mohammad S. "More on μ-semi-Lindelöf sets in μ-spaces." Demonstratio Mathematica 54, no. 1 (January 1, 2021): 259–71. http://dx.doi.org/10.1515/dema-2021-0026.

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Abstract Sarsak [On μ \mu -compact sets in μ \mu -spaces, Questions Answers Gen. Topology 31 (2013), no. 1, 49–57] introduced and studied the class of μ \mu -Lindelöf sets in μ \mu -spaces. Mustafa [ μ \mu -semi compactness and μ \mu -semi Lindelöfness in generalized topological spaces, Int. J. Pure Appl. Math. 78 (2012), no. 4, 535–541] introduced and studied the class of μ \mu -semi-Lindelöf sets in generalized topological spaces (GTSs); the primary purpose of this paper is to investigate more properties and mapping properties of μ \mu -semi-Lindelöf sets in μ \mu -spaces. The class of μ \mu -semi-Lindelöf sets in μ \mu -spaces is a proper subclass of the class of μ \mu -Lindelöf sets in μ \mu -spaces. It is shown that the property of being μ \mu -semi-Lindelöf is not monotonic, that is, if ( X , μ ) \left(X,\mu ) is a μ \mu -space and A ⊂ B ⊂ X A\subset B\subset X , where A A is μ B {\mu }_{B} -semi-Lindelöf, then A A need not be μ \mu -semi-Lindelöf. We also introduce and study a new type of generalized open sets in GTSs, called ω μ {\omega }_{\mu } -semi-open sets, and investigate them to obtain new properties and characterizations of μ \mu -semi-Lindelöf sets in μ \mu -spaces.

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Prokop, Frank P. "Neighbourhood lattices – a poset approach to topological spaces." Bulletin of the Australian Mathematical Society 39, no. 1 (February 1989): 31–48. http://dx.doi.org/10.1017/s0004972700027969.

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In this paper neighbourhood lattices are developed as a generalisation of topological spaces in order to examine to what extent the concepts of “openness”, “closedness”, and “continuity” defined in topological spaces depend on the lattice structure of P(X), the power set of X.A general pre-neighbourhood system, which satisfies the poset analogues of the neighbourhood system of points in a topological space, is defined on an ∧-semi-lattice, and is used to define open elements. Neighbourhood systems, which satisfy the poset analogues of the neighbourhood system of sets in a topological space, are introduced and it is shown that it is the conditionally complete atomistic structure of P(X) which determines the extension of pre-neighbourhoods of points to the neighbourhoods of sets.The duals of pre-neighbourhood systems are used to generate closed elements in an arbitrary lattice, independently of closure operators or complementation. These dual systems then form the backdrop for a brief discussion of the relationship between preneighbourhood systems, topological closure operators, algebraic closure operators, and Čech closure operators.Continuity is defined for functions between neighbourhood lattices, and it is proved that a function f: X → Y between topological spaces is continuous if and only if corresponding direct image function between the neighbourhood lattices P(X) and P(Y) is continuous in the neighbourhood sense. Further, it is shown that the algebraic character of continuity, that is, the non-convergence aspects, depends only on the properites of pre-neighbourhood systems. This observation leads to a discussion of the continuity properties of residuated mappings. Finally, the topological properties of normality and regularity are characterised in terms of the continuity properties of the closure operator on a topological space.

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Mršević, M., I. L. Reilly, and M. K. Vamanamurthy. "On semi-regularization topologies." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 38, no. 1 (February 1985): 40–54. http://dx.doi.org/10.1017/s1446788700022588.

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AbstractThis paper discusses several properties of topological spaces and how they are refelected by corresponding properties of the associated semi-regularization topologies. For example a space is almost locally connected if and only if its semi-regularization is locally connected. Various separation, connectedness, covering, and mapping properties are considered.

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FARAJZADEH, A. P. "ON PSEUDOMONOTONE SET-VALUED MAPPINGS IN TOPOLOGICAL VECTOR SPACES." ANZIAM Journal 50, no. 2 (October 2008): 258–65. http://dx.doi.org/10.1017/s144618110900008x.

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Farajzadeh, A. P., A. Amini-Harandi, and D. O'Regan. "Existence Results for Generalized Vector Equilibrium Problems with Multivalued Mappings via KKM Theory." Abstract and Applied Analysis 2008 (2008): 1–8. http://dx.doi.org/10.1155/2008/968478.

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We first define upper sign continuity for a set-valued mapping and then we consider two types of generalized vector equilibrium problems in topological vector spaces and provide sufficient conditions under which the solution sets are nonempty and compact. Finally, we give an application of our main results. The paper generalizes and improves results obtained by Fang and Huang in (2005).

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Huang, Jianhua. "The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces." Journal of Mathematical Analysis and Applications 312, no. 1 (December 2005): 374–82. http://dx.doi.org/10.1016/j.jmaa.2005.03.040.

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Chen, Yu-Qing. "Fixed points for convex continuous mappings in topological vector spaces." Proceedings of the American Mathematical Society 129, no. 7 (November 21, 2000): 2157–62. http://dx.doi.org/10.1090/s0002-9939-00-05767-1.

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Yuan, George Xian-Zhi. "Fixed points of upper semicontinuous mappings in locally G-convex spaces." Bulletin of the Australian Mathematical Society 58, no. 3 (December 1998): 469–78. http://dx.doi.org/10.1017/s0004972700032457.

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In this paper a new fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values is established in the setting of an abstract convex structure – called a locally G-convex space, which generalises usual convexity such as locally convex H-spaces, locally convex spaces (locally H-convex spaces), hyperconvex metric spaces and locally convex topological spaces. Our fixed point theorem includes corresponding Fan-Glicksberg type fixed point theorems in locally convex H-spaces, locally convex spaces, hyperconvex metric space and locally convex spaces in the existing literature as special cases.

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Boudhraa, Zineddine. "D-Spaces and Resolution." Canadian Mathematical Bulletin 40, no. 4 (December 1, 1997): 395–401. http://dx.doi.org/10.4153/cmb-1997-047-5.

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AbstractA space X is a D-space if, for every neighborhood assignment f there is a closed discrete set D such that f(D) = X. In this paper we give some necessary conditions and some sufficient conditions for a resolution of a topological space to be a D-space. In particular, if a space X is resolved at each x ∊ X into a D-space Yx by continuous mappings fx: X − {x} → Yx, then the resolution is a D-space if and only if {x} × Bd(Yx) is a D-space.

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Husain, Shamshad, and Sanjeev Gupta. "Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings." Filomat 26, no. 5 (2012): 909–16. http://dx.doi.org/10.2298/fil1205909h.

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In this paper, we introduce and study a class of generalized nonlinear vector quasi-variational- like inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalized mixed quasi-variational-like inequalities and so on. By means of fixed point theorem, we obtain existence theorem of solutions to the class of generalized nonlinear vector quasi-variational-like inequalities in the setting of locally convex topological vector spaces.

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Gupta, Ankit, and Ratna Dev Sarma. "A study of topological structures on equi-continuous mappings." Proyecciones (Antofagasta) 40, no. 2 (April 2021): 335–54. http://dx.doi.org/10.22199/issn.0717-6279-2021-02-0020.

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Function space topologies are developed for EC(Y,Z), the class of equi-continuous mappings from a topological space Y to a uniform space Z. Properties such as splittingness, admissibility etc. are defined for such spaces. The net theoretic investigations are carried out to provide characterizations of splittingness and admissibility of function spaces on EC(Y,Z). The open-entourage topology and pointtransitive-entourage topology are shown to be admissible and splitting respectively. Dual topologies are defined. A topology on EC(Y,Z) is found to be admissible (resp. splitting) if and only if its dual is so.

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Paul, Avinoy. "On some new paranormed sequence spaces defined by the matrix (D )(r,0,0,s)." Proyecciones (Antofagasta) 40, no. 3 (June 1, 2021): 779–96. http://dx.doi.org/10.22199/issn.0717-6279-4321.

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In this paper, we introduce some new paranormed sequence spaces and study some topological properties. Further, we determine α, β and γ-duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of matrix mappings.

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Mauro, Guilherme V. S., Luiza A. Moraes, and Alex F. Pereira. "Topological and algebraic properties of spaces of Lorch analytic mappings." Mathematische Nachrichten 289, no. 7 (November 5, 2015): 845–53. http://dx.doi.org/10.1002/mana.201400108.

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Karamian, Ardeshir, and Rahmatollah Lashkaripour. "Existence of solutions for a new version of generalized operator equilibrium problems." Filomat 32, no. 13 (2018): 4701–10. http://dx.doi.org/10.2298/fil1813701k.

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In this paper, a system of generalized operator equilibrium problems(for short, SGOEP) in the setting of topological vector spaces is introduced. Applying some properties of the nonlinear scalarization mapping and the maximal element lemma an existence theorem for SGOEP is proved. Moreover, using Ky Fan?s lemma an existence result for the generalized operator equilibrium problem(for short, GOEP) is established. The results of the paper can be viewed as a generalization and improvement of the corresponding results given in [1,2,5,8].

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Fawakhreh, A. J., and A. Kiliçman. "Mappings and decompositions of continuity on almost Lindelöf spaces." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–7. http://dx.doi.org/10.1155/ijmms/2006/98760.

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A topological spaceXis said to be almost Lindelöf if for every open cover{Uα:α∈Δ}ofXthere exists a countable subset{αn:n∈ℕ}⊆Δsuch thatX=∪n∈ℕCl(Uαn). In this paper we study the effect of mappings and some decompositions of continuity on almost Lindelöf spaces. The main result is that a image of an almost Lindelöf space is almost Lindelöf.

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Ferraro, Mario, and David H. Foster. "Differentiation of fuzzy continuous mappings on fuzzy topological vector spaces." Journal of Mathematical Analysis and Applications 121, no. 2 (February 1987): 589–601. http://dx.doi.org/10.1016/0022-247x(87)90259-9.

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Lally, Nick, and Luke Bergmann. "Mapping dynamic, non-Euclidean spaces." Abstracts of the ICA 1 (July 15, 2019): 1–2. http://dx.doi.org/10.5194/ica-abs-1-204-2019.

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Abstract. Space is often described as a dynamic entity in human geographic theory, one that resists being pinned down to static representations. Co-produced in and through relations between various things and phenomena, space in these accounts is variously described as being contingent, processual, plastic, relational, situated, topological, and uneven. In contrast, most cartographic methods and tools are based on static, Euclidean understandings of space that can be reduced to a simple, mathematical description. In this work, I explore how cartography can deal with space as a dynamic and fluid concept that is entangled with the phenomena and objects being mapped. To those ends, I describe a method for creating animated maps based on relational understandings of space that are always in flux.This work builds on research in collaboration with Luke Bergmann, where we suggest a move from Geographic Information Systems (GIS) as we commonly know them to the broader realm of geographical imagination systems (gis) that are informed by spatial theory in human geography. The animated maps here are produced using our prototype gis software Enfolding, which use multidimensional scaling (MDS) to visualize relational spaces, in combination with Blender, an open-source 3D rendering program. Written in JavaScript and available as open source software, Enfolding is our first attempt to make gis an accessible set of tools that expand the possibilities for mapping by providing new grammars for creative cartographic practices.In the cartographic workflow presented here, I use Enfolding to produce manifolds from a set of points and user-defined distances between points. Changing those measures of distance &ndash; which might represent travel times, affective connections, communicative links, or any other relationship as defined by a user &ndash; produces shifting manifolds. Using the .obj export option in Enfolding, I then import the manifolds into Blender, using them as animation keyframes. In Figure 1, I have added a digital elevation model (DEM) to the 3D figure, producing an animated visualization of a dynamic and relational space that includes a hillshade.This workflow represents only one of many creative possibilities for innovative cartographic practices that engage with space as a matter of concern. With growing interest in 3D cartographic methods comes expanded possibilities for visualizing dynamic and relational spaces. Combining conceptual antecedents in both human and quantitative geography with current cartographic methods allows for new approaches to both mapping and space. The workflow and tools that have emerged from this research are presented here with the hope of spurring creative and exploratory cartographic work that draws from but also contributes to vibrant discussions in spatial theory and creative cartography.

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Moors, Warren B., and Sivajah Somasundaram. "Usco selections of densely defined set-valued mappings." Bulletin of the Australian Mathematical Society 65, no. 2 (April 2002): 307–13. http://dx.doi.org/10.1017/s0004972700020347.

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A set-valued mapping Φ : X → 2Y acting between topological spaces X and Y is said to be “lower demicontinuous” if the interior of the closure of the set Φ−1(V): = {x ∈ X : Φ(x) ∩ V ≠ ∅} is dense in the closure of Φ−1(V) for each open set V in Y. Čoban, Kenderov and Revalski (1994) showed that for every densely defined lower demicontinuous mapping Φ acting from a Baire space X into subsets of a monotonely Čech-complete space Y, there exist a dense and Gδ subset X1 ⊆ X and an usco mapping G: X1 → 2Y such that G (x) ⊆ Φ*(x), for every x ∈ X1, where the mapping Φ*: X → 2Y is the extension of Φ defined by, W is a neighbourhood of x}.In this paper we present a proof of the above result with the notion of monotone Čcech-completeness replaced by the weaker notion of partition completeness. In addition, we observe that if the range space also lies is Stegall's class then we may assume that the mapping G is single-valued on X1.

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Hu, Yu-da, and Chen Ling. "A Class of Cone Bounded Quasiconvex Mappings in Topological Vector Spaces." Acta Mathematicae Applicatae Sinica, English Series 19, no. 4 (November 1, 2003): 611–20. http://dx.doi.org/10.1007/210255-003-0135-x.

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Mirzoyan, M. M. "Limit sets, continuity, and uncertainty points of mappings of topological spaces." Doklady Mathematics 73, no. 2 (June 2006): 221–22. http://dx.doi.org/10.1134/s1064562406020189.

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Journal articles on the topic 'Mapping (Mathematics) Topological spaces'

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