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Mathematics > Group Theory
Title: The Baire property and precompact duality
(Submitted on 4 May 2024)
Abstract: We prove that if $G$ is a totally bounded abelian group \st\ its dual group $\widehat{G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco, Dom\'inguez and Tkachenko. {Among other consequences, we obtain an example of a group that is $g$-dense in its completion but is not $g$-barrelled. This solves a question proposed by Au${\beta}$enhofer and Dikranjan.}
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