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Minimal sequential Hausdorff spaces
International Journal of Mathematics and Mathematical Sciences, 2004 A sequential space (X, T) is called minimal sequential if no sequential topology on X is strictly weaker than T. This paper begins the study of minimal sequential Hausdorff spaces. Characterizations of minimal sequential Hausdorff spaces are obtained using filter bases, sequences, and functions satisfying certain graph conditions.
Bhamini M. P. Nayar
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On countable choice and sequential spaces [PDF]
Mathematical Logic Quarterly, 2008 AbstractUnder the axiom of choice, every first countable space is a Fréchet‐Urysohn space. Although, in its absence even ℝ may fail to be a sequential space.Our goal in this paper is to discuss under which set‐theoretic conditions some topological classes, such as the first countable spaces, the metric spaces, or the subspaces of ℝ, are classes of ...
Gonçalo Gutierres
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Sequential Completeness for ⊤-Quasi-Uniform Spaces and a Fixed Point Theorem
Mathematics, 2022 We define sequential completeness for ⊤-quasi-uniform spaces using Cauchy pair ⊤-sequences. We show that completeness implies sequential completeness and that for ⊤-uniform spaces with countable ⊤-uniform bases, completeness and sequential completeness ...
Gunther Jäger
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Sequential order of product spaces
Topology and Its Applications, 1995 This paper investigates the sequential order of the products of sequential spaces. The following are main results in this paper. Here, for a sequential space \(X\), let \(so (X)\) be the sequential order of \(X\). Also, for a space \(X\), let \(S(X)\) be the sequential coreflection of \(X\); that is, \(S[X]\) is a new space having a sequential closure ...
Tsugunori Nogura, Alexander Shibakov
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Some Properties of Lebesgue Fuzzy Metric Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2021 In this paper, we establish a sequential characterisation of Lebesgue fuzzy metric and explore the relationship between Lebesgue, weak $G$-complete and compact fuzzy metric spaces.
Sugata Adhya, Atasi Deb Ray
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Further aspects of I K-convergence in topological spaces
Applied General Topology, 2021 In this paper, we obtain some results on the relationships between different ideal convergence modes namely, I K, I K∗ , I, K, I ∪ K and (I ∪K) ∗ . We introduce a topological space namely I K-sequential space and show that the class of I K-sequential ...
Ankur Sharmah, Debajit Hazarika
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G-sequential methods in product spaces
AIP Conference Proceedings, 2022 © 2022 American Institute of Physics Inc.. All rights reserved.It is known that for a Hausdorff topological space X the limits of convergent sequences in X determines a function from the set of all convergent sequences in X to X. This notion has been extended in [14] by Connor and Grosse-Erdmann to a real valued function defined on a liner subspace of ...
Behram, Shanza, Mucuk, Osman
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Advances in Mathematical Physics, 2021 In this paper, the notion of sequential ςp-metric spaces has been introduced as a generalization of usual S-metric spaces, Sb-metric spaces, SJS metric spaces, and specially of Sp-metric spaces.
Abdollah Karami +2 more
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Concrete functors that respect initiality and finality
Applied General Topology, 2023 We study concrete endofunctors of the category of convergence spaces and continuous maps that send initial maps to initial maps or final maps to final maps. The former phenomenon turns out to be fairly common while the latter is rare.
Frédéric Mynard
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Some Fixed-Point Theorems over a Generalized F-Metric Space
Advances in Mathematical Physics, 2021 In this article, the concept of sequential F-metric spaces has been introduced as a generalization of usual metric spaces, b-metric spaces, JS-metric spaces, and mainly F-metric spaces. Some topological properties of such spaces have been discussed here.
Kushal Roy +4 more
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