Pseudocompact group topologies with prescribed topological subspaces
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Other documents of the author: Galindo, Jorge; García Ferreira, S.; Tomita, Artur Hideyuki
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
Pseudocompact group topologies with prescribed topological subspacesDate
2009Publisher
International Society for Mathematical SciencesISSN
1346-0447Type
info:eu-repo/semantics/articlePublisher version
http://www.jams.or.jp/notice/scmjol/2009.htmlVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
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 ... [+]
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. If, for instance, G is an Abelian group with m(β) ≤ r0(G) ≤ |G| ≤ 2β (see
the Introduction below for unexplained terminology) for some uncountable cardinal β,
and X is any topological space with |X| ≤ r0(G) and w(X) ≤ β, then G admits a
pseudocompact topological group topology that contains X as a subspace.
If, on the other direction, G is a torsion Abelian group that admits a pseudocompact
group topology, then, for every sequence (an)n∈ of G there exists a pseudocompact
group topology on G for which some subsequence of (an)n∈ converges. [-]
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Scientiae Mathematicae Japonicae Online, e-2009 , 22, p. 427–436Rights
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