Topological automorphisms of modified Sierpiński gaskets realize arbitrary finite permutation groups
type: Item
instance of: scholarly article
title: Topological automorphisms of modified Sierpiński gaskets realize arbitrary finite permutation groups
zbMATH Open document ID: 0948.51012
DOI: 10.1016/S0166-8641(98)00118-7
author: Reinhard Winkler
published in: Topology and its Applications
publication date: 2000-11-19T00:00:00Z
review text: In this interesting note some topological properties of \(n\)-dimensional Sierpiński gaskets \(X\) are investigated. The author shows that (for \(n\geq 2\)) every topological automorphism of \(X\) is one of the \((n+1)!\) symmetries acting as the symmetric group on the vertex set of the underlying simplex. Furthermore it is shown that for a given finite subgroup of \(S_{n+1}\) there is a finite subset \(T\subseteq X\) such that \(G\) is the group of topological automorphisms of \(X\setminus T\) considered as a group acting faithfully on the vertices.
Mathematics Subject Classification ID: 51H99
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 1395051
zbMATH Keywords: Sierpiński gaskets
zbMATH Keywords: topological automorphism
reviewed by: Robert F. Tichy
MaRDI profile type: Publication
full work available at URL: s0166-8641(98)00118-7
OpenAlex ID: W2032298354
description: scientific article; zbMATH DE number 1395051