Work

The Baire property and precompact duality

Year: 2024

Type: article

Abstract: We prove that if G G is a totally bounded Abelian group such that its dual group G ^ p \widehat {G}_p equipped with the finite-open topology is a Baire group, then every compact subset of G 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 g -dense in its completion but is not g g -barreled. This solves a question proposed by Außenhofer and Dikranjan.

Source: Proceedings of the American Mathematical Society Series B

DOI: 10.1090/bproc/245

Authors: M. Ferrer, S. Hernández, I. Sepúlveda, F. Trigos-Arrieta

Institutions: Universitat Jaume I, California State University, Bakersfield

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $750

Funders: Ministerio de Economía y Competitividad, Universitat Jaume I, Ministerio de Ciencia y Tecnología, Agencia Estatal de Investigación