Results 91 to 100 of about 116 (108)
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Applied Categorical Structures, 2007
A Tychonoff space is \textit{weakly pseudocompact} in case it is \(G_{\delta}\)-dense in some of its compactifications [\textit{S. Garcia-Ferreira} and \textit{A. Garcia-Maynez}, ``On weakly-pseudocompact spaces'', Houston J. Math. 20, No. 1, 145--159 (1994; Zbl 0809.54012)]. In the present paper, the authors extend the notion of weak pseudocompactness
Dube, Themba, Walters-Wayland, Joanne
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A Tychonoff space is \textit{weakly pseudocompact} in case it is \(G_{\delta}\)-dense in some of its compactifications [\textit{S. Garcia-Ferreira} and \textit{A. Garcia-Maynez}, ``On weakly-pseudocompact spaces'', Houston J. Math. 20, No. 1, 145--159 (1994; Zbl 0809.54012)]. In the present paper, the authors extend the notion of weak pseudocompactness
Dube, Themba, Walters-Wayland, Joanne
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Proper Pseudocompact Subgroups of Pseudocompact Abelian Groups
Annals of the New York Academy of Sciences, 1994ABSTRACT: We prove among other things that if G is a pseudocompact Abelian topological group such that |G| > c or ω1≤w(G)≤ c then G has a proper dense pseudocompact subgroup.
W. W. COMFORT +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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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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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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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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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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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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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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