The Baire property and precompact duality

2024/05/04 by Ferrer, M., Hernández, S., Sepúlveda, I. +1
#Commutative Algebra (math.AC) #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2405.02624

Abstract

We prove that if G is a totally bounded abelian group \st its dual group \widehatG_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, Domínguez 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 Auβenhofer and Dikranjan.

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