Pseudocompact group topologies with no infinite compact subsets
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Pseudocompact group topologies with no infinite compact subsetsData de publicació
2010-05Cita bibliogràfica
arXiv:0812.5033v3Tipus de document
info:eu-repo/semantics/articleVersió
info:eu-repo/semantics/sumittedVersionParaules clau / Matèries
Resum
We show that every Abelian group satisfying a mild cardi-
nal inequality admits a pseudocompact group topology from which all
countable subgroups inherit the maximal totally bounded topology (we
say that such a ... [+]
We show that every Abelian group satisfying a mild cardi-
nal 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 re-
flexive precompact groups that are not compact. [-]
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