Results 81 to 90 of about 117 (105)
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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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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
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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1990
In this paper we study the spaces for which the topology generated by the A-closure is pseudocompact.
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In this paper we study the spaces for which the topology generated by the A-closure is pseudocompact.
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Pseudocompact Topological Groups
2018Topological groups constitute a very special subclass of topological spaces. Every topological group satisfying the \(T_0\) separation axiom is automatically Tychonoff, which means that in the class of topological groups, the axioms of separation \(T_0\), \(T_1\), \(T_2\), \(T_3\) and \(T_{3.5}\) are all equivalent.
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