A generalization of the open mapping theorem and a possible generalization of the Baire category theorem

DOI10.1016/J.TOPOL.2023.108594zbMATH Open1530.22004arXiv2205.10443OpenAlexW4377019800WikidataQ120913834 ScholiaQ120913834MaRDI QIDQ6098398

Antoni Machowski

Publication date: 13 June 2023

Published in: Topology and its Applications (Search for Journal in Brave)

Abstract: We characterize continuum as the smallest cardinality of a family of compact sets needed to cover a locally compact group for which the Open Mapping Theorem does not hold.

Full work available at URL: https://arxiv.org/abs/2205.10443

zbMATH Keywords

topological groupLie grouplocally compactopen mapping theoremBaire category theoremsigma-compact

Mathematics Subject Classification ID

General properties and structure of locally compact groups (22D05) Cardinal characteristics of the continuum (03E17)

Cites Work

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• The Lie theory of connected pro-Lie groups. A structure theory for pro-Lie algebras, pro-Lie groups, and connected locally compact groups
• Topological groups and related structures
• The structure of locally compact groups
• A generalization of a theorem of Gleason
• The Baire category theorem and cardinals of countable cofinality
• Independence results concerning the number of nowhere dense sets necessary to cover the real line
• The structure of compact groups. A primer for the student -- a handbook for the expert

Related Items (1)

Open mappings of locally compact groups

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