Pseudocompact group topologies with prescribed topological subspaces
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Títol
Pseudocompact group topologies with prescribed topological subspacesData de publicació
2009Editor
International Society for Mathematical SciencesISSN
1346-0447Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://www.jams.or.jp/notice/scmjol/2009.htmlVersió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
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. [-]
Publicat a
Scientiae Mathematicae Japonicae Online, e-2009 , 22, p. 427–436Drets d'accés
Copyright (C), International Society for Mathematical Sciences
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info:eu-repo/semantics/openAccess
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
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