Topological groups with several disconnectedness

2001/06/13 by Masasi Higasikawa, Higasikawa, Masasi
Decision Sciences · Mathematics · #22A05 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Rings, Modules, and Algebras #math.GN #msc:22A05

paper · pdf · doi:10.48550/arxiv.math/0106105

12 pages

arxiv created 2001/06/13 · openalex publication_date 2001/06/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of non-Archimedeanness are obtained by using embedding into universal groups. We also clarify the differences between the properties by constructing miscellaneous Polish groups.

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