Pseudocompact group topologies with no infinite compact subsets
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comunitat-uji-handle2:10234/7037
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http://dx.doi.org/10.1016/j.jpaa.2010.06.014 |
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Title
Pseudocompact group topologies with no infinite compact subsetsDate
2011Publisher
ElsevierISSN
0022-4049Bibliographic citation
Journal of Pure and Applied Algebra (Apr. 2011) vol. 215, no. 4, p. 655-663Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0022404910001271Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
We show that every Abelian group satisfying a mild cardinal inequality admits a pseudocompact group topology from which all countable subgroups inherit the maximal totally bounded topology (we say that such a topolo ... [+]
We show that every Abelian group satisfying a mild cardinal inequality admits a pseudocompact group topology from which all countable subgroups inherit the maximal totally bounded topology (we say that such a topology satisfies property ).
Every pseudocompact Abelian group G with cardinality |G|≤22c satisfies this inequality and therefore admits a pseudocompact group topology with property . Under the Singular Cardinal Hypothesis (SCH) this criterion can be combined with an analysis of the algebraic structure of pseudocompact groups to prove that every pseudocompact Abelian group admits a pseudocompact group topology with property .
We also observe that pseudocompact Abelian groups with property contain no infinite compact subsets and are examples of Pontryagin reflexive precompact groups that are not compact. [-]
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