Thin and bounded subsets of free topological groups
type: Item
instance of: scholarly article
title: Thin and bounded subsets of free topological groups
zbMATH Open document ID: 0712.22001
DOI: 10.1016/0166-8641(90)90005-M
author: Ol'ga Sipacheva
author: Mikhail Tkachenko
published in: Topology and its Applications
publication date: 1990-01-01T00:00:00Z
review text: A subset A of a topological group G is said to be thin in G if for any open neighbourhood U of the identity there exists an open neighbourhood V of the identity such that \(xVx^{-1}\) is a subset of U, for all x in A. This notion was introduced by the second author [Sib. Mat. Zh. 25, 146- 158 (1984; 536.22003)] to construct special topologies on free groups. In this paper the authors find necessary and sufficient conditions for thinness of subsets of Markov free topological groups.
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54B05
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54G10
zbMATH DE Number: 4171239
zbMATH Keywords: P-space
zbMATH Keywords: thinness of subsets
zbMATH Keywords: Markov free topological groups
reviewed by: Sidney A. Morris
MaRDI profile type: Publication
cites work: Pseudocompactness and uniform continuity in topological groups
cites work: Q4150804
cites work: The Cofinal Character of Uniform Spaces and Ordered Fields
cites work: Q3320595
cites work: Q3684320
cites work: Compactness type properties in topological groups
description: scientific article; zbMATH DE number 4171239