Groups of homeomorphisms and normal subgroups of the group of permutations
type: Item
instance of: scholarly article
title: Groups of homeomorphisms and normal subgroups of the group of permutations
zbMATH Open document ID: 0751.54016
DOI: 10.1155/S0161171291000650
author: P. T. Ramachandran
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1992-06-26T00:00:00Z
full work available at URL: https://eudml.org/doc/46725
review text: The main result is: no nontrivial proper normal subgroup of the group of permutations of a fixed set \(X\) can be the group of autohomeomorphisms of \((X,T)\) for any topology (without any additional properties) \(T\) on \(X\). For comparison, recall that any group is isomorphic to the group of all autohomeomorphisms of a topological space [\textit{J. de Groot}, Math. Ann. 138, 80--102 (1959; Zbl 0087.37802)].
Mathematics Subject Classification ID: 54H15
Mathematics Subject Classification ID: 54F99
zbMATH DE Number: 22385
zbMATH Keywords: homeomorphism
zbMATH Keywords: homogeneous space
zbMATH Keywords: permutation
reviewed by: Michael Megrelishvili
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 22385