Results 1 to 10 of about 97 (86)
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.
A V Arhangel'Skii
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Selectively Pseudocompact Groups without Infinite Separable Pseudocompact Subsets
Axioms, 2018 We give a “naive” (i.e., using no additional set-theoretic assumptions beyond ZFC, the Zermelo-Fraenkel axioms of set theory augmented by the Axiom of Choice) example of a Boolean topological group G without infinite separable pseudocompact subsets ...
Dmitri Shakhmatov, Víctor Hugo Yañez
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Topology and Its Applications, 1998 The paper is full of interesting results on pseudocompact spaces. The main result generalizes Comfort-Ross theorems [\textit{W. W. Comfort} and \textit{K. A. Ross}, Pac. J. Math. 16, 483-496 (1966; Zbl 0214.28502)]: (1) Every product of pseudocompact Mal'tsev spaces is pseudocompact; (2) If \(X\) is a pseudocompact Mal'tsev space, then every Mal'tsev ...
Reznichenko, E.A., Uspenskij, V.V.
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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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A connected pseudocompact space
Topology and Its Applications, 1994 In this article a space \(X\) is called pseudocompact if every discrete collection of open subsets of \(X\) is finite. Recall that a set \(A\) is said to be conditionally compact or relatively countably compact in a space \(X\) if every infinite subset of \(A\) has a limit point in \(X\). At the 1990 Summer Conference in General Topology at Long Island
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A NOTE ON Cc(X) VIA A TOPOLOGICAL RING [PDF]
Journal of Algebraic Systems, 2023 Let $C_c(X)$ (resp., $C_c^*(X)$) denote the functionallycountable subalgebra of $C(X)$ (resp., $C^*(X)$),consisting of all functions (resp., bounded functions) with countable image.$C_c(X)$ (resp., $C_c^*(X)$) as a topological ring via $m_c$-topology ...
R. Mohamadian +3 more
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Maximal pseudocompact spaces and the Preiss-Simon property
Open Mathematics, 2014 Alas Ofelia +2 more
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m-TOPOLOGY ON THE RING OF REAL-MEASURABLE FUNCTIONS [PDF]
Journal of Algebraic Systems, 2021 In this article we consider the $m$-topology on \linebreak $M(X,\mathscr{A})$, the ring of all real measurable functions on a measurable space $(X, \mathscr{A})$, and we denote it by $M_m(X,\mathscr{A})$.
H. Yousefpour +3 more
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Topology and Its Applications, 1994 It is shown that if \(X,Y\) are Tychonoff pseudocompact spaces, then every continuous real-valued function on \(X \times Y\) can be extended to a separately continuous function on \(\beta (X) \times \beta (Y)\). Using this result (which has its own interest the author proves that any Tychonoff pseudocompact group \(G\) with continuous multiplication is
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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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