More on topological \(N\)-groups
type: Item
instance of: scholarly article
title: More on topological \(N\)-groups
zbMATH Open document ID: 0809.22003
DOI: 10.1007/BF02573675
published in: Semigroup Forum
publication date: 1995-03-29T00:00:00Z
full work available at URL: https://eudml.org/doc/135317
review text: A topological group \(G\) is admissible if it is locally compact and Hausdorff and, in addition, satisfies the following condition: for each pair \(A, B\) of disjoint closed subsets of \(G\) and each pair of distinct points \(a, b \in G\), there exists a continuous selfmap \(f\) of \(G\) such that \(f[A] = a\) and \(f[B] = b\). The author discusses conditions under which a connected admissible topological group is topologically isomorphic to \(R^ m\) (the \(m\)-fold cartesian product of the group of real numbers) or to \(T^ m\) (the \(m\)-fold cartesian product of the circle group).
Mathematics Subject Classification ID: 22A05
zbMATH DE Number: 549069
zbMATH Keywords: compact-open topology
zbMATH Keywords: continuous selfmap
zbMATH Keywords: connected admissible topological group
zbMATH Keywords: group of real numbers
zbMATH Keywords: circle group
author: jun. Kenneth D. Magill
reviewed by: John A. Hildebrant
MaRDI profile type: Publication
cites work: Q5522002
cites work: Q4032146
cites work: Topological \(N\)-groups
cites work: Q3671335
OpenAlex ID: W2914671033
description: scientific article; zbMATH DE number 549069