Character and pseudocharacter in minimal topological groups
type: Item
instance of: scholarly article
title: Character and pseudocharacter in minimal topological groups
zbMATH Open document ID: 0594.22001
DOI: 10.1007/BF01157021
author: B. George
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: For any uncountable cardinal \(\tau\) the author constructs a (totally) minimal topological group G with \(\psi (G)=\aleph_ 0\) and \(\chi (G)=\tau\). Thus he answers in the negativ the well-known question rised by A. V. Arkhangel'skij whether the pseudocharacter and the character of each minimal topological group coincide. Morover, an elegant author's construction shows that for any free group H with \(| H| =\tau \geq \aleph_ 0\) there exists a totally minimal topological group topology \({\mathcal T}\) on H such that \(\psi\) (H,\({\mathcal T})=\aleph_ 0\) and \(\chi\) (H,\({\mathcal T})=\tau\). The problem of Arkhangel'skij was also solved independently by I. I. Guran and V. G. Pestov.
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 3955260
zbMATH Keywords: group of bijections
zbMATH Keywords: minimal topological group
zbMATH Keywords: pseudocharacter
zbMATH Keywords: character
zbMATH Keywords: free group
reviewed by: Mikhail Tkachenko
MaRDI profile type: Publication
cites work: Q5645625
cites work: Q3885938
cites work: Q4155096
cites work: Q3039589
cites work: Q3963056
description: scientific article; zbMATH DE number 3955260