A generalization of the Open Mapping Theorem and a possible generalization of the Baire Category Theorem

2022/05/20 by Antoni Machowski, Machowski, Antoni
Computer Science · Mathematics · #22D05 (Primary) 03E17(Secondary) #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2205.10443

openalex publication_date 2022/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Open mappings of locally compact groups
• Topology, Metric Spaces and the Generalized Continuum Hypothesis
• Every Continuum has a Compact Universal Cover
• Less than continuum many translates of a compact nullset may cover any infinite profinite group
• The number of translates of a closed nowhere dense set required to cover a Polish group