Results 11 to 20 of about 212 (106)
On the maximal G-compactification of products of two G-spaces
International Journal of Mathematics and Mathematical Sciences, 2006 Let G be any Hausdorff topological group and let βGX denote the maximal G-compactification of a G-Tychonoff space X. We prove that if X and Y are two G-Tychonoff spaces such that the product X×Y is pseudocompact, then βG(X×Y)=βGX×βGX.
Natella Antonyan
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Extremal α-pseudocompact abelian groups [PDF]
Forum Mathematicum, 2009 For a cardinal k, generalizing a recent result of Comfort and van Mill, we prove that every k-pseudocompact abelian group of weight >k has some proper dense k-pseudocompact subgroup and admits some strictly finer k-pseudocompact group topology.
GIORDANO BRUNO, Anna
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Extremal pseudocompact Abelian groups are compact metrizable [PDF]
Proceedings of the American Mathematical Society, 2007 Every pseudocompact Abelian group of uncountable weight has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology.
Comfort, W.W., van Mill, J.
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Pseudocompact group topologies with no infinite compact subsets [PDF]
Journal of Pure and Applied Algebra, 2011 19 pages; In this version we work assuming SCH (Singular Cardinal Hypothesis), whereas in our previous version we had to assume GCH (Generalized Continuum Hypothesis). The general problem is still open in ZFC, but models avoiding SCH are much harder to come by. We thank professors W. W. Comfort and D. Dikranjan for their help concerning Example 5.9.
Galindo, Jorge, Macario, Sergio
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Abelian torsion groups with a pseudocompact group topology [PDF]
Forum Mathematicum, 1994 Two questions are posed: (a) Which Abelian torsion groups admit a PGT (pseudocompact group topology)? (b) If an Abelian torsion group G admits a PGT, for which cardinal numbers a may such a topology F be chosen so that the weight of the space > G,F > is equal to a? The authors answer question (a) completely (Theorems 3.17 and 3.19).
COMFORT, W.W., Remus, Dieter
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On the supremum of the pseudocompact group topologies
Topology and its Applications, 2008 A topological space on which each real valued continuous function is bounded is called pseudocompact. Let \textbf{P} be the class of pseudocompact Hausdorff topological groups, and \({\mathbf P}'\) the class of groups \(G\) admitting a topology \({\mathcal T}\) such that \((G,{\mathcal T})\in{\mathbf P}\).
Comfort, W.W., van Mill, J.
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The group of characters of a pseudocompact locally compact semitopological semigroup
Applied General TopologyWe prove that each semitopological semigroup has a reflection in the class of abelian cancellative semitopological semigroups. Then we use this reflection to prove that the group of characters of a locally compact pseudocompact topological semigroup with
Julio César Hernández Arzusa
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Three examples of pseudocompact quasitopological groups
Topology and its Applications, 2006 It is known that the product of an arbitrary family of pseudocompact topological groups is pseudocompact and both a topological group of countable cellularity and a pseudocompact topological group are Moscow spaces, where a space \(X\) is called \textit{Moscow} if the closure of every open subset of \(X\) is the union of a family of \(G_{\delta}\)-sets
Hernández, C., Tkachenko, M.
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Pseudocompact group topologies with prescribed topological subspaces [PDF]
Scientiae Mathematicae Japonicae, 2009 We prove that every pseudocompact topological Abelian group G admits a pseudocompact topological group topology with a non-trivial convergent sequence. Imposing some restrictions on the properties of G, stronger properties are also obtained.
Galindo, Jorge +2 more
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Making group topologies with, and without, convergent sequences [PDF]
Applied General Topology, 2006 (1) Every infinite, Abelian compact (Hausdorff) group K admits 2|K|- many dense, non-Haar-measurable subgroups of cardinality |K|. When K is nonmetrizable, these may be chosen to be pseudocompact. (2) Every infinite Abelian group G admits a family A of
W.W. Comfort +2 more
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