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Relevant bibliographies by topics / Tychonoff space

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Academic literature on the topic 'Tychonoff space'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Tychonoff space"

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ALZahrani, Samirah. "C-Tychonoff and L-Tychonoff Topological Spaces." European Journal of Pure and Applied Mathematics 11, no. 3 (July 31, 2018): 882–92. http://dx.doi.org/10.29020/nybg.ejpam.v11i3.3253.

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A topological space X is called C-Tychonoff if there exist a one-to-one function f from X onto a Tychonoff space Y such that f restriction K from K onto f(K) is a homeomorphism for each compact subspace K of X. We discuss this property and illustrate the relationships between C-Tychonoffness and some other properties like submetrizability, local compactness, L-Tychononess, C-normality, C-regularity, epinormality, sigma-compactness, pseudocompactness and zero-dimensional.

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Shakhmatov, Dimitri, Mikhail Tkachenko, Vladimir V. Tkachuk, and Richard G. Wilson. "Strengthening connected Tychonoff topologies." Applied General Topology 3, no. 2 (October 1, 2002): 113. http://dx.doi.org/10.4995/agt.2002.2058.

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<p>The problem of whether a given connected Tychonoff space admits a strictly finer connected Tychonoff topology is considered. We show that every Tychonoff space X satisfying ω (X) ≤ c and c (X) ≤ N<sub>0</sub> admits a finer strongly σ-discrete connected Tychonoff topology of weight 2<sup>c</sup>. We also prove that every connected Tychonoff space is an open continuous image of a connected strongly σ-discrete submetrizable Tychonoff space. The latter result is applied to represent every connected topological group as a quotient of a connected strongly σ-discrete submetrizable topological group.</p>

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Tzannes, V. "A Tychonoff non-normal space." International Journal of Mathematics and Mathematical Sciences 16, no. 3 (1993): 615–16. http://dx.doi.org/10.1155/s0161171293000754.

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A Tychonoff non-normal space is constructed which can be used for the construction of a regular space on which every weakly continuous (hence everyθ-continuous orη-continuous) map into a given space is constant.

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Rice, Michael D. "Reflexive objects in topological categories." Mathematical Structures in Computer Science 6, no. 4 (August 1996): 375–86. http://dx.doi.org/10.1017/s0960129500001079.

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This paper presents several basic results about the non-existence of reflexive objects in cartesian closed topological categories of Hausdorff spaces. In particular, we prove that there are no non-trivial countably compact reflexive objects in the category of Hausdorff k-spaces and, more generally, that any non-trivial reflexive Tychonoff space in this category contains a closed discrete subspace corresponding to a numeral system in the sense of Wadsworth. In addition, we establish that a reflexive Tychonoff space in a cartesian-closed topological category cannot contain a non-trivial continuous image of the unit interval. Therefore, if there exists a non-trivial reflexive Tychonoff space, it does not have a nice geometric structure.

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Basu, C. K., and S. S. Mandal. "Maximal Tychonoff spaces and normal isolator covers." Publications de l'Institut Math?matique (Belgrade) 99, no. 113 (2016): 217–25. http://dx.doi.org/10.2298/pim1613217b.

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We introduce a new kind of cover called a normal isolator cover to characterize maximal Tychonoff spaces. Such a study is used to provide an alternative proof of an interesting result of Feng and Garcia-Ferreira in 1999 that every maximal Tychonoff space is extremally disconnected. Maximal tychonoffness of subspaces is also discussed.

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Gabriyelyan, S. S. "Free Locally Convex Spaces and the k-space Property." Canadian Mathematical Bulletin 57, no. 4 (December 1, 2014): 803–9. http://dx.doi.org/10.4153/cmb-2014-019-7.

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AbstractLet L(X) be the free locally convex space over a Tychonoff space X. Then L(X) is a k-space if and only if X is a countable discrete space. We prove also that L(D) has uncountable tightness for every uncountable discrete space D.

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Çoker, Doğan, A. Haydar Eş, and Necla Turanli. "A Tychonoff theorem in intuitionistic fuzzy topological spaces." International Journal of Mathematics and Mathematical Sciences 2004, no. 70 (2004): 3829–37. http://dx.doi.org/10.1155/s0161171204403603.

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The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some characterizations concerning fuzzy compactness. Lastly we give a Tychonoff-like theorem.

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Jumaev, D. "(O-C)-compact Spaces and Hyperspaces Functor." Bulletin of Science and Practice 5, no. 4 (April 15, 2019): 30–37. http://dx.doi.org/10.33619/2414-2948/41/03.

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In the work, it is established that the space of all nonempty compact subsets of a Tychonoff space is (O-C)–compact if and only if the give Tychonoff space is (O-C)–compact. Further, for a map f:X→Y the map expβX→Y is (O-C)–compact if and only if the map f is (O-C)–compact.

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Kocinac, Ljubisa. "On spaces of group-valued functions." Filomat 25, no. 2 (2011): 163–72. http://dx.doi.org/10.2298/fil1102163k.

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Elfard, Ali Sayed. "Neighborhood base at the identity of free paratopological groups." Topological Algebra and its Applications 1 (November 12, 2013): 31–36. http://dx.doi.org/10.2478/taa-2013-0004.

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AbstractIn 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.

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Dissertations / Theses on the topic "Tychonoff space"

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Stover, Derrick D. "Continuous Mappings and Some New Classes of Spaces." 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:3371579.

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Törnkvist, Robin. "Tychonoff's theorem and its equivalence with the axiom of choice." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-107423.

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In this essay we give an elementary introduction to topology so that we can prove Tychonoff’s theorem, and also its equivalence with the axiom of choice.
Denna uppsats tillhandahåller en grundläggande introduktion till topologi för att sedan bevisa Tychonoff’s theorem, samt dess ekvivalens med urvalsaxiomet.

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Book chapters on the topic "Tychonoff space"

1

Tozzi, A., and V. Trnková. "Clone Segments of the Tychonoff Modification of Space." In Papers in Honour of Bernhard Banaschewski, 327–37. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-017-2529-3_19.

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Buskes, Gerard, and Arnoud van Rooij. "Tychonoff’s Theorem." In Topological Spaces, 270–82. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0665-1_17.

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Sanchis, M. "Bounded Subsets of Tychonoff Spaces: A Survey of Results and Problems." In Pseudocompact Topological Spaces, 107–50. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91680-4_4.

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Boules, Adel N. "Essentials of General Topology." In Fundamentals of Mathematical Analysis, 191–244. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198868781.003.0005.

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The first eight sections of this chapter constitute its core and are generally parallel to the leading sections of chapter 4. Most of the sections are brief and emphasize the nonmetric aspects of topology. Among the topics treated are normality, regularity, and second countability. The proof of Tychonoff’s theorem for finite products appears in section 8. The section on locally compact spaces is the transition between the core of the chapter and the more advanced sections on metrization, compactification, and the product of infinitely many spaces. The highlights include the one-point compactification, the Urysohn metrization theorem, and Tychonoff’s theorem. Little subsequent material is based on the last three sections. At various points in the book, it is explained how results stated for the metric case can be extended to topological spaces, especially locally compact Hausdorff spaces. Some such results are developed in the exercises.

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