Rigid sets in the Hilbert cube
type: Item
instance of: scholarly article
title: Rigid sets in the Hilbert cube
zbMATH Open document ID: 0587.54022
DOI: 10.1016/0166-8641(86)90080-5
author: J. Lamoreaux
author: David G. Wright
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: An embedding of a compact metric space X into the Hilbert cube is said to be rigid provided the only homeomorphism of X to itself that extends to a homeomorphism of the Hilbert cube is the identity homeomorphism. Evidently, a space C that has an isolated point cannot have a rigid embedding into the Hilbert cube. The authors show that this is the only ''obstruction'' by showing that if a compact metric space X has no isolated points, then X has uncountably many distinct rigid embeddings into the Hilbert cube. This work extends earlier work, in the finite dimensional setting, of the second author and, as that work was, is based on an analysis of ''essentially'' distinct wild embeddings of the Cantor set.
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 57N35
Mathematics Subject Classification ID: 57N20
Mathematics Subject Classification ID: 54E45
zbMATH DE Number: 3942450
zbMATH Keywords: rigid subspace
zbMATH Keywords: Hilbert cube
zbMATH Keywords: Cantor set
MaRDI profile type: Publication
full work available at URL: 0166-8641(86)90080-5
OpenAlex ID: W2083468528
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description: scientific article; zbMATH DE number 3942450