Relevant bibliographies by topics / Compact spaces. Topological spaces. Topology

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Compact spaces. Topological spaces. Topology'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Compact spaces. Topological spaces. Topology"

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Kovár, Martin Maria. "The Classes of Mutual Compactificability." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–11. http://dx.doi.org/10.1155/2007/16135.

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Two disjoint topological spacesX,Yare mutually compactificable if there exists a compact topology onK=X∪Ywhich coincides onX,Ywith their original topologies such that the pointsx∈X,y∈Yhave disjoint neighborhoods inK. The main problem under consideration is the following: which spacesX,Yare so compatible such that they together can form the compact spaceK? In this paper we define and study the classes of spaces with the similar behavior with respect to the mutual compactificability. Two spacesX1,X2belong to the same class if they can substitute each other in the above construction with any spaceY. In this way we transform the main problem to the study of relations between the compactificability classes. Some conspicuous classes of topological spaces are discovered as the classes of mutual compactificability. The studied classes form a certain “scale of noncompactness” for topological spaces. Every class of mutual compactificability contains aT1representative, but there are classes with no Hausdorff representatives.
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Ozturk, Taha Yasin, and Sadi Bayramov. "Soft Mappings Space." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/307292.

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Various soft topologies are being introduced on a given function space soft topological spaces. In this paper, soft compact-open topology is defined in functional spaces of soft topological spaces. Further, these functional spaces are studied and interrelations between various functional spaces with soft compact-open topology are established.
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BHATTACHARJEE, PAPIYA. "TWO SPACES OF MINIMAL PRIMES." Journal of Algebra and Its Applications 11, no. 01 (February 2012): 1250014. http://dx.doi.org/10.1142/s0219498811005373.

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This paper studies algebraic frames L and the set Min (L) of minimal prime elements of L. We will endow the set Min (L) with two well-known topologies, known as the Hull-kernel (or Zariski) topology and the inverse topology, and discuss several properties of these two spaces. It will be shown that Min (L) endowed with the Hull-kernel topology is a zero-dimensional, Hausdorff space; whereas, Min (L) endowed with the inverse topology is a T1, compact space. The main goal will be to find conditions on L for the spaces Min (L) and Min (L)-1 to have various topological properties; for example, compact, locally compact, Hausdorff, zero-dimensional, and extremally disconnected. We will also discuss when the two topological spaces are Boolean and Stone spaces.
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Aurichi, Leandro F., and Rodrigo R. Dias. "Topological Games and Alster Spaces." Canadian Mathematical Bulletin 57, no. 4 (December 1, 2014): 683–96. http://dx.doi.org/10.4153/cmb-2013-048-5.

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AbstractIn this paper we study connections between topological games such as Rothberger, Menger, and compact-open games, and we relate these games to properties involving covers byGδsubsets. The results include the following: (1) If TWO has a winning strategy in theMenger game on a regular spaceX, thenXis an Alster space. (2) If TWO has a winning strategy in the Rothberger game on a topological spaceX, then theGδ-topology onXis Lindelöf. (3) The Menger game and the compact-open game are (consistently) not dual.
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Georgiou, D. N., and B. K. Papadopoulos. "On nearly compact topological and fuzzy topological spaces." Topology and its Applications 123, no. 1 (August 2002): 73–85. http://dx.doi.org/10.1016/s0166-8641(01)00171-7.

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Bardyla, Serhii, and Alex Ravsky. "Closed subsets of compact-like topological spaces." Applied General Topology 21, no. 2 (October 1, 2020): 201. http://dx.doi.org/10.4995/agt.2020.12258.

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<p>We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We show that each Hausdorff topological space is a closed subspace of some Hausdorff ω-bounded pracompact topological space and describe open dense subspaces of<br />countably pracompact topological spaces. We construct a pseudocompact topological semigroup which contains the bicyclic monoid as a closed subsemigroup. This example provides an affirmative answer to a question posed by Banakh, Dimitrova, and Gutik in [4]. Also, we show that the semigroup of ω×ω-matrix units cannot be embedded into a Hausdorff topological semigroup whose space is weakly H-closed.</p>
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Gabriyelyan, Saak S., and Sidney A. Morris. "Embedding into free topological vector spaces on compact metrizable spaces." Topology and its Applications 233 (January 2018): 33–43. http://dx.doi.org/10.1016/j.topol.2017.09.008.

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Coquand, Thierry. "Minimal invariant spaces in formal topology." Journal of Symbolic Logic 62, no. 3 (September 1997): 689–98. http://dx.doi.org/10.2307/2275567.

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A standard result in topological dynamics is the existence of minimal subsystem. It is a direct consequence of Zorn's lemma: given a compact topological space X with a map f: X→X, the set of compact non empty subspaces K of X such that f(K) ⊆ K ordered by inclusion is inductive, and hence has minimal elements. It is natural to ask for a point-free (or formal) formulation of this statement. In a previous work [3], we gave such a formulation for a quite special instance of this statement, which is used in proving a purely combinatorial theorem (van de Waerden's theorem on arithmetical progression).In this paper, we extend our analysis to the case where X is a boolean space, that is compact totally disconnected. In such a case, we give a point-free formulation of the existence of a minimal subspace for any continuous map f: X→X. We show that such minimal subspaces can be described as points of a suitable formal topology, and the “existence” of such points become the problem of the consistency of the theory describing a generic point of this space. We show the consistency of this theory by building effectively and algebraically a topological model. As an application, we get a new, purely algebraic proof, of the minimal property of [3]. We show then in detail how this property can be used to give a proof of (a special case of) van der Waerden's theorem on arithmetical progression, that is “similar in structure” to the topological proof [6, 8], but which uses a simple algebraic remark (Proposition 1) instead of Zorn's lemma. A last section tries to place this work in a wider context, as a reformulation of Hilbert's method of introduction/elimination of ideal elements.
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Al-shami, T. M. "Sum of the spaces on ordered setting." Moroccan Journal of Pure and Applied Analysis 6, no. 2 (December 1, 2020): 255–65. http://dx.doi.org/10.2478/mjpaa-2020-0020.

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AbstractOne of the divergences between topology and ordered topology is that some topological concepts such as separation axioms and continuous maps are defined using open neighborhoods or neighborhoods without any difference, however, they are distinct on the ordered topology according to the neighborhoods: Are they open neighborhoods or not? In this paper, we present the concept of sum of the ordered spaces using pairwise disjoint topological ordered spaces and study main properties. Then, we introduce the properties of ordered additive, finitely ordered additive and countably ordered additive which associate topological ordered spaces with their sum. We prove that the properties of being Ti-ordered and strong Ti-ordered spaces are ordered additive, however, the properties of monotonically compact and ordered compact spaces are finitely ordered additive. Also, we define a mapping between two sums of the ordered spaces using mappings between the ordered spaces and deduce some results related to some types of continuity and homeomorphism. We complete this work by determining the conditions under which a topological ordered space is sum of the ordered spaces.
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Latif, Raja Mohammad. "Infra -α- Compact and Infra -α- Connected Spaces." International Journal of Pure Mathematics 8 (August 11, 2021): 41–57. http://dx.doi.org/10.46300/91019.2021.8.6.

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In 2016 Hakeem A. Othman and Md. Hanif Page introduced a new notion of set in general topology called an infra -α- open set and investigated its fundamental properties and studied the relationship between infra -α- open set and other topological sets. The objective of this paper is to introduce the new concepts called infra -α- compact space, countably infra -α- compact space, infra -α- Lindelof space, almost infra -α- compact space, mildly infra -α- compact space and infra -α- connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.
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Dissertations / Theses on the topic "Compact spaces. Topological spaces. Topology"

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Ntantu, Ibula. "The compact-open topology on C(X)." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/76467.

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This paper investigates the compact-open topology on the set of Ck(X) of continuous real-valued functions defined on a Tychonoff space X. More precisely, we study the following problem: If P is a topological property, does there exist a topological property Q so that Ck(X) has P if and only if X has Q? Characterizations of many properties are obtained throughout the thesis, sometimes modulo some “mild” restrictions on the space X. The main properties involved are summarized in a diagram in the introduction.
Ph. D.
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Dolph, Bosely Laura. "Applications of elementary submodels in topology." View abstract, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3372301.

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Bailey, Bradley S. "I-weight, special base properties and related covering properties." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Fall/Dissertation/BAILEY_BRADLEY_37.pdf.

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Price, Ray Hampton. "The property B(P,[alpha])-refinability and its relationship to generalized paracompact topological spaces." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/49871.

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The property B(P,∝)-refinability is studied and is used to obtain new covering characterizations of paracompactness, collectionwise normality, subparacompactness, d-paracompactness, a-normality, mesocompactness, and related concepts. These new characterizations both generalize and unify many well-known results. The property B(P,∝)-refinability is strictly weaker than the property Θ-refinability. A B(P,∝)-refinement is a generalization of a σ-locally finite-closed refinement. Here ∝ is a fixed ordinal which dictates the number of "levels" in a given refinement, and P represents a property such as discreteness or local finiteness which each "level" must satisfy relative to a certain subspace.
Ph. D.
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Kolat, Alycia M. "Topological Function Spaces." Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1314380881.

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Al, Mahrouqi Sharifa. "Compact topological spaces inspired by combinatorial constructions." Thesis, University of East Anglia, 2013. https://ueaeprints.uea.ac.uk/43361/.

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Due to Mrówka [24], polyadic spaces are compact Hausdorff spaces that are continuous images of some power of the one point compactification αλ of a discrete space λ. It turns out that many results about polyadic spaces hold for a more general class spaces, as we shall show in this thesis. For a sequence ‾λ = {λᵢ:iΕI} of cardinals, a compact Hausdorff space X is λ‾-multiadic if it is a continuous image of Πᵢ_ΕIαλᵢ. It is easy to observe that a λ‾-multiadic space is λ-polyadic, but whether the converse is true is a motivation of this dissertation. Although the individual polyadic and multiadic spaces differ, we show that the class of polyadic spaces is the same as multiadic class! Moreover, this dissertation is concerned with the combinatorics of multiadic class that can be used to give some of their topological structure. We give a Ramsey-like property for the class of multiadic compacta called Qλ where λ is a regular cardinal. For Boolean spaces this property is equivalent to the following: every uncountable collection of clopen sets contains an uncountable subcollection which is either linked or disjoint. We give generalizations of the Standard Sierpiński graph and use them to show that the property of being κ-multiadic is not inherited by regular closed sets for arbitrarily large κ.
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Pinchuck, Andrew. "Extension theorems on L-topological spaces and L-fuzzy vector spaces." Thesis, Rhodes University, 2002. http://hdl.handle.net/10962/d1005219.

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A non-trivial example of an L-topological space, the fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.
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Miller, David. "Homotopy theory for stratified spaces." Thesis, University of Aberdeen, 2010. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=158352.

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There are many different notions of stratified spaces. This thesis concerns homotopically stratified spaces. These were defined by Frank Quinn in his paper Homotopically Stratified Sets ([16]). His definition of stratified space is very general and relates strata by “homotopy rather than geometric conditions”. This makes homotopically stratified spaces the ideal class of stratified spaces on which to define and study stratified homotopy theory. In the study of stratified spaces it is useful to examine spaces of popaths (paths which travel from lower strata to higher strata) and holinks (those spaces of popaths which immediately leave a lower stratum for their final stratum destination). It is not immediately clear that for adjacent strata these two path spaces are homotopically equivalent and even less clear that this equivalence can be constructed in a useful way. The first aim of this thesis is to prove such an equivalence exists for homotopically stratified spaces. We will define stratified analogues of the usual definitions of maps, homotopies and homotopy equivalences. Then we will provide an elementary criterion for deciding when a strongly stratified map is a stratified homotopy equivalence. This criterion states that a strongly stratified map is a stratified homotopy equivalence if and only if the induced maps on strata and holink spaces are homotopy equivalences. Using this criterion we will prove that any homotopically stratified space is stratified homotopy equivalent to a homotopically stratified space where neighborhoods of strata are mapping cylinders. Finally we will develop categorical descriptions of the class of homotopically stratified spaces up to stratified homotopy. The first of these categorical descriptions will involve categories with a topology on their object and morphism sets. The second categorical description will involve only categories with discrete object spaces.
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Lamont, Julie. "Total negation in general topology and in ordered topological spaces." Thesis, Queen's University Belfast, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334503.

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Chishwashwa, Nyumbu. "Pairings of Binary reflexive relational structures." Thesis, University of the Western Cape, 2008. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_7126_1256734489.

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The main purpose of this thesis is to study the interplay between relational structures and topology , and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations between the categories of topological spaces, closure spaces and relational structures. We study the 4-point non-Hausdorff model S4 weakly homotopy equivalent to the circle S1. We study pairings of some objects in the category of relational structures similar to the multiplication S4 x S4- S4 S4 fails to be order preserving for posets. Nevertheless, applying a single barycentric subdivision on S4 to get S8, an 8-point model of the circle enables us to define an order preserving poset map S8 x S8- S4. Restricted to the axes, this map yields weak homotopy equivalences S8 x S8, we obtain a version of the Hopf map S8 x S8s - SS4. This model of the Hopf map is in fact a map of non-Hausdorff double map cylinders.

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Books on the topic "Compact spaces. Topological spaces. Topology"

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Topological methods in Euclidean spaces. Mineola, N.Y: Dover Publications, 2000.

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James, I. M. Topological and uniform spaces. New York: Springer-Verlag, 1987.

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Arthur, Seebach J., ed. Counterexamples in topology. New York: Dover Publications, 1995.

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Nagata, Jun-iti. Modern general topology. 2nd ed. Amsterdam: North-Holland, 1985.

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Teleiko, A. Categorical topology of compact Hausdorff spaces. Edited by Zarichnyi M. Lviv, Ukraine: VNTL Publishers, 1999.

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A, Sutherland W. Introduction to metric and topological spaces. 2nd ed. Oxford: Oxford University Press, 2009.

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Introduction to metric and topological spaces. 2nd ed. Oxford: Oxford University Press, 2009.

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1953-, Ntantu Ibula, ed. Topological properties of spaces of continuous functions. Berlin: Springer-Verlag, 1988.

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Barmak, Jonathan A. Algebraic topology of finite topological spaces and applications. Heidelberg: Springer, 2011.

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Barmak, Jonathan A. Algebraic Topology of Finite Topological Spaces and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22003-6.

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Book chapters on the topic "Compact spaces. Topological spaces. Topology"

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Voigt, Jürgen. "Initial Topology, Topological Vector Spaces, Weak Topology." In Compact Textbooks in Mathematics, 1–9. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-32945-7_1.

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Singh, Tej Bahadur. "Topological Spaces." In Introduction to Topology, 1–28. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6954-4_1.

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Buskes, Gerard, and Arnoud van Rooij. "Transition to Topology." In Topological Spaces, 171–84. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0665-1_11.

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James, I. M. "Compact Spaces." In Topological and Uniform Spaces, 62–70. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-4716-6_6.

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Adamson, Iain T. "Topological Spaces." In A General Topology Workbook, 3–18. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-0-8176-8126-5_1.

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Buskes, Gerard, and Arnoud van Rooij. "What Topology Is About." In Topological Spaces, 3–22. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0665-1_1.

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Naber, Gregory L. "Topological Spaces." In Topology, Geometry, and Gauge Fields, 27–100. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4757-2742-5_2.

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Waldmann, Stefan. "Topological Spaces and Continuity." In Topology, 5–40. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09680-3_2.

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Waldmann, Stefan. "Construction of Topological Spaces." In Topology, 41–57. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09680-3_3.

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Waldmann, Stefan. "Convergence in Topological Spaces." In Topology, 59–71. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09680-3_4.

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Conference papers on the topic "Compact spaces. Topological spaces. Topology"

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Parimala, M., D. Arivuoli, R. Perumal, and S. Krithika. "nIαg-Compact spaces and nIαg-Lindelof spaces in nano ideal topological spaces." In 1ST INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2020. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0025274.

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Kalaivani, N., D. Saravanakumar, and T. Gunasekar. "Operation-connected spaces, compact spaces with α(γ,γ′) - Open sets in topological spaces." In THE 11TH NATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5112210.

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Feledziak, Krzysztof. "Weakly compact operators on Köthe-Bochner spaces with the mixed topology." In Function Spaces VIII. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc79-0-5.

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Xiao, Yan, Bingxin Wang, and Hui Sun. "Quantitative analysis of the topologic morphology of urban street network based on system coupling theory." In Post-Oil City Planning for Urban Green Deals Virtual Congress. ISOCARP, 2020. http://dx.doi.org/10.47472/eogp1958.

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Researchers are increasingly paying attention to urban morphology to address problems regarding urban form and to sustain the development of urban economy, society, and environments. A preliminary research framework was built to conduct coupling analyses on street form and block functions. These analyses are implemented using a planar graph method and using quantitative descriptions of the urban streets functions, but the coupling relation of street morphology and block function cannot be well defined, and it often cannot be analyzed in multi-level and multi-scale. Along with two proposed measuring parameters (connectivity and accessibility of coupling networks), the framework was used to quantitatively analyze the coupling coordination degree of the topologic morphology and functional structure of block samples for various urban streets. Through empirical research on different samples from Dalian, China, we validated the operability and urban street network coupling analysis in different spatial regions in built environments. This technique can be used to study the overall spatial morphology and design urban streets at different scales and scopes. Further, it helps recognize the space and cultural connotations of urban streets via spatial coupling, compare different urban textures, and predict design results to foster discussions on the optimization of urban planning design schemes.
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Aquilué, Inés, Estanislao Roca, and Javier Ruiz. "Topological analysis of contemporary morphologies under conflict: The urban transformation of Dobrinja in Sarajevo and the Central District of Beirut." In 24th ISUF 2017 - City and Territory in the Globalization Age. Valencia: Universitat Politècnica València, 2017. http://dx.doi.org/10.4995/isuf2017.2017.6167.

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Regarding topological interpretation of space, this research aims to identify urban morphologies, whose topology becomes increasingly determining under high uncertainty. This topological approach has been applied in an evolutionary analysis of urban spaces under siege, fear and conflict, which conducted to the construction of a specific method. This method analyses the transformation of urban areas in five consecutive phases: urban form [1], increase of uncertainty [2], application of the apparatus [3], change in urban form [4], information flows [5]. These five phases were applied to different empirical studies, analysed through specific morphological and topological models. In the light of this method, two selected urban morphologies Dobrinja –a suburb in Sarajevo– and the Beirut Central District have been examined. The urban morphology of both areas was dramatically transformed after both civil conflicts –the Bosnian War and the Lebanese Civil War–. Dobrinja suffered severe modifications, first provoked by the violence of the siege during the Bosnian War [1992-1995], and then by the Inter-Entity Boundary Line as a result of the Dayton Peace Agreement [December 1995], which divided the neighbourhood and caused serious alterations in its ethno-demographic and spatial structure. The Beirut Central District was first destroyed by the violence experienced in the Lebanese Civil War [1975-1990] and then by the process of subsequent reconstruction [since 1992], which led to a simplification of its structure. The two morphological and topological analyses enable us to determine the initial causes and their spatial consequences in both urban areas, regarding their conflict and post-conflict stage.
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