The Baire property and precompact duality
Group Theory
2024-05-07 v1 Commutative Algebra
General Topology
Abstract
We prove that if is a totally bounded abelian group \st\ its dual group equipped with the finite-open topology is a Baire group, then every compact subset of 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 -dense in its completion but is not -barrelled. This solves a question proposed by Auenhofer and Dikranjan.}
Cite
@article{arxiv.2405.02624,
title = {The Baire property and precompact duality},
author = {M. Ferrer and S. Hernández and I. Sepúlveda and F. J. Trigos-Arrieta},
journal= {arXiv preprint arXiv:2405.02624},
year = {2024}
}