Results 131 to 140 of about 560 (152)
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Pseudocompactness and resolvability
Fundamenta Mathematicae, 2018In this clearly written paper the authors prove that every crowded pseudocompact Tychonoff space of cellularity at most the continuum is resolvable. Recall that a \textit{crowded space} is a topological space without isolated points. A crowded space is \textit{resolvable} [\textit{E. Hewitt}, Duke Math. J.
Ortiz-Castillo, Y. F., Tomita, A. H.
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Topology and Its Applications, 1994 It is proved that a Tychonoff pseudocompact group with continuous multiplication is a topological group. It is also proved that a Tychonoff countably compact group with separately continuous multiplication is a topological group.
Reznichenko, E.A.
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Russian Mathematical Surveys, 1985
The relationships between pseudocompact, countably compact and Baire spaces are investigated. Let \(\chi\) be a cover of a set Y and \(X\subseteq Y\). We put \(St^ 1(X,\gamma)=\cup \{V\in \gamma: V\cap X\neq \emptyset \}\) and \(St^{k+1}(X,\gamma)=St(St^ k(X,\gamma),\gamma)\) for each \(k\in {\mathbb{N}}\).
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The relationships between pseudocompact, countably compact and Baire spaces are investigated. Let \(\chi\) be a cover of a set Y and \(X\subseteq Y\). We put \(St^ 1(X,\gamma)=\cup \{V\in \gamma: V\cap X\neq \emptyset \}\) and \(St^{k+1}(X,\gamma)=St(St^ k(X,\gamma),\gamma)\) for each \(k\in {\mathbb{N}}\).
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Ultrafilters, monotone functions and pseudocompactness
Archive for Mathematical Logic, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael Hrusák +2 more
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Pseudocompactness and Ultrafilters
2018Since Hewitt (Trans Amer Math Soc 64:54–99 1948, [21]) introduced the notion of pseudocompactness, topologists have generalized or modified it to obtain many new concepts. Our main goal in this survey article is to study some topological and combinatorial aspects of certain pseudocompactness-like properties.
S. García-Ferreira +1 more
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2018
A well known result established by Hewitt (Trans Amer Math Soc 64:45–99 1948, [16]) states that a space X is pseudocompact if and only if X is \(G_\delta \)-dense in \(\beta X\). In Garcia-Ferreira and Garcia-Maynez (Houston J Math 20(1):145–159, 1994, [12]), S. Garcia-Ferreira and A.
A. Dorantes-Aldama +2 more
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A well known result established by Hewitt (Trans Amer Math Soc 64:45–99 1948, [16]) states that a space X is pseudocompact if and only if X is \(G_\delta \)-dense in \(\beta X\). In Garcia-Ferreira and Garcia-Maynez (Houston J Math 20(1):145–159, 1994, [12]), S. Garcia-Ferreira and A.
A. Dorantes-Aldama +2 more
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Mathematica Slovaca, 2015
Abstract The cozero part of a sigma-frame is considered here for the first time. The fundamental notion of a trail in a frame is adapted for sigma-frames via the notion of a witness and, as a consequence, one obtains characterisations for the cozero elements, and of pseudocompactness, of sigma-frames.
Jumani Clarke, Christopher Gilmour
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Abstract The cozero part of a sigma-frame is considered here for the first time. The fundamental notion of a trail in a frame is adapted for sigma-frames via the notion of a witness and, as a consequence, one obtains characterisations for the cozero elements, and of pseudocompactness, of sigma-frames.
Jumani Clarke, Christopher Gilmour
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2018
If \(\mathcal {P}\) is a topological property and \(\mathcal C\) is a class of topologies, then a space X is said to be maximal \(\mathcal {P}\) in the class \(\mathcal C\) if X has \(\mathcal {P}\) but no strictly stronger topology on X which belongs to the class \(\mathcal C\) has \(\mathcal {P}\).
M. Madriz-Mendoza +2 more
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If \(\mathcal {P}\) is a topological property and \(\mathcal C\) is a class of topologies, then a space X is said to be maximal \(\mathcal {P}\) in the class \(\mathcal C\) if X has \(\mathcal {P}\) but no strictly stronger topology on X which belongs to the class \(\mathcal C\) has \(\mathcal {P}\).
M. Madriz-Mendoza +2 more
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Some Generalizations of Pseudocompactness
Annals of the New York Academy of Sciences, 1994ABSTRACT: In this paper, we introduce the concepts of p‐boundedness for pɛω*, (α, M)‐pseudocompactness and (α, M)‐compactness, for a cardinal number α and Ø≠M⊆β(ω)\ω. We prove that Xα is pseudocompact (respectively, countably compact) iff X is (α, M)‐pseudocompact (respectively, (α, M)‐compact), for some Ø≠M⊆β(ω)\ω; the Rudin‐Keisler order on β(ω)\ω ...
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Siberian Mathematical Journal, 2001
We consider the problem of extending the notion of τ-pseudocompactness from spaces to continuous mappings, obtain conditions under which the product of τ-pseudocompact mappings is τ-pseudocompact. Since any space X can be considered as a continuous mapping from X into a singleton, we obtain consequences of the theorems on multiplicativity of τ ...
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We consider the problem of extending the notion of τ-pseudocompactness from spaces to continuous mappings, obtain conditions under which the product of τ-pseudocompact mappings is τ-pseudocompact. Since any space X can be considered as a continuous mapping from X into a singleton, we obtain consequences of the theorems on multiplicativity of τ ...
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