Results 1 to 10 of about 77 (75)
Spaces whose Pseudocompact Subspaces are Closed Subsets
Applied General Topology, 2004 Every first countable pseudocompact Tychonoff space X has the property that every pseudocompact subspace of X is a closed subset of X (denoted herein by “FCC”).
Alan Dow +3 more
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Applied General Topology, 2021 Let C∞ (X) denote the family of real-valued continuous functions which vanish at infinity in the sense that {x ∈ X : |f(x)| ≥ 1/n} is compact in X for all n ∈ N. It is not in general true that C∞ (X) is an ideal of C(X).
Biswajit Mitra, Debojyoti Chowdhury
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Strongly τ-pseudocompact spaces
Topology and its Applications, 1998 All hypothesized spaces are Tychonoff, and \(\tau\) is an infinite cardinal number. The author introduces the concept of a strongly \(\tau\)-pseudocompact space, studies its relation to initial \(\tau\)-compactness, and extends results of [\textit{J. F. Kennison}, Trans. Am. Math. Soc. 104, 436-442 (1962; Zbl 0111.35004)] and others.
Sanchis, Manuel +1 more
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Closed subsets of compact-like topological spaces
Applied General Topology, 2020 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 ...
Serhii Bardyla, Alex Ravsky
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Few remarks on maximal pseudocompactness
Applied General Topology, 2018 A pseudocompact space is maximal pseudocompact if every strictly finer topology is no longer pseudocompact. The main result here is a counterexample which answers a question rised by Alas, Sanchis and Wilson.
Angelo Bella
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A note on bf-spaces and on the distribution of the functor of the Dieudonné completion
Topological Algebra and its Applications, 2021 A subset B of a space X is said to be bounded (in X) if the restriction to B of every real-valued continuous function on X is bounded. A real-valued function on X is called bf-continuous if its restriction to each bounded subset of X has a continuous ...
Sanchis Manuel, Valero Óscar
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Pseudocompact and precompact topological subsemigroups of topological groups
Pracì Mìžnarodnogo Geometričnogo Centru, 2023 It is known that every pseudocompact topological group is precompact, we extend this result to a class of subsemigroup of topological groups. Then we use this results to prove that cancellative locally compact countably compact topological semigroups ...
Julio Cesar Hernandez
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مجلة جامعة الانبار للعلوم الصرفة, 2009 Lindelof spaces, using multifunctions, are given.Our main results are .A space X is z-compact iff for every space Y and z-closed graph multifunction on X into Y the image of every z-closed set in X, is closed in Y. A space X is z-Lindelof iff for every P-
Atallah Th. Al-Ani
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Intermediate rings of complex-valued continuous functions
Applied General Topology, 2021 For a completely regular Hausdorff topological space X, let C(X, C) be the ring of complex-valued continuous functions on X, let C ∗ (X, C) be its subring of bounded functions, and let Σ(X, C) denote the collection of all the rings that lie between C ...
Amrita Acharyya +3 more
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Ascoli’s theorem for pseudocompact spaces [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020 A Tychonoff space $X$ is called ({\em sequentially}) {\em Ascoli} if every compact subset (resp. convergent sequence) of $C_k(X)$ is equicontinuous, where $C_k(X)$ denotes the space of all real-valued continuous functions on $X$ endowed with the compact-open topology. The classical Ascoli theorem states that each compact space is Ascoli. We show that a
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