Some \((n-1)\)-dimensional rigid sets in \(\mathbb{R}^ n\)
type: Item
instance of: scholarly article
title: Some \((n-1)\)-dimensional rigid sets in \(\mathbb{R}^ n\)
zbMATH Open document ID: 0803.54029
DOI: 10.1007/BF01610622
author: Irmina Herburt
published in: Geometriae Dedicata
publication date: 1994-05-18T00:00:00Z
review text: The author considers subsets of Euclidean \(n\)-space which are geometrically acceptable as metric spaces in the sense of \textit{K. Borsuk} [Bull. Pol. Acad. Sci., Math. 29, 83-90 (1981; Zbl 0459.54020)]. Such a subset is called rigid if every intrinsic isometry is the restriction of an isometry of the ambient space. Here it is shown that rigidity of a subset is preserved if a countable number of points are removed from its interior. This leads to a construction of \((n-1)\)-dimensional rigid subsets of Euclidean \(n\)-space. The examples given in this paper are non- compact.
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 569283
zbMATH Keywords: intrinsic isometry
reviewed by: Bernd Wegner
MaRDI profile type: Publication
cites work: Q3909690
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description: scientific article; zbMATH DE number 569283