Pontryagin duality in the class of precompact Abelian groups and the Baire property
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hdl:2117/16724
Tipus de documentArticle
Data publicació2012
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Abstract
We present a wide class of reflexive, precompact, non-compact,
Abelian topological groups G determined by three requirements. They
must have the Baire property, satisfy the open refinement condition,
and contain no infinite compact subsets. This combination of properties
guarantees that all compact subsets of the dual group G∧ are
finite. We also show that many (non-reflexive) precompact Abelian
groups are quotients of reflexive precompact Abelian groups. This includes
all precompact almost metrizable groups with the Baire property
and their products. Finally, given a compact Abelian group G of
weight ≥ 2!, we find proper dense subgroups H1 and H2 of G such
that H1 is reflexive and pseudocompact, while H2 is non-reflexive and
almost metrizable.
CitacióBruguera, M.; Tkachenko, M. Pontryagin duality in the class of precompact Abelian groups and the Baire property. "Journal of pure and applied algebra", 2012, vol. 216, núm. 12, p. 2636-2647.
ISSN0022-4049
Versió de l'editorhttp://arxiv.org/pdf/1101.4504v1.pdf
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