Every topological group is a group retract of a minimal group

2006/10/06 by Michael Megrelishvili, Megrelishvili, Michael
Mathematics · #22A05 #54H11 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Rings, Modules, and Algebras #math.FA #math.GN #msc:22A05 #msc:54H11

paper · pdf · doi:10.48550/arxiv.math/0610226

22 pages

arxiv created 2006/10/06 · openalex publication_date 2006/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that every Hausdorff topological group is a group retract of a minimal topological group. This first was conjectured by Pestov in 1983. Our main result leads to a solution of some problems of Arhangelskii. One of them is the problem about representability of a group as a quotient of a minimal group (Problem 519 in the first edition of "Open Problems in Topology"). Our approach is based on generalized Heisenberg groups and on groups arising from group representations on Banach spaces and in bilinear mappings.

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