Techniques and examples in U-embedding
type: Item
instance of: scholarly article
title: Techniques and examples in U-embedding
zbMATH Open document ID: 0603.54017
DOI: 10.1016/0166-8641(86)90006-4
author: Ronnie Levy
author: Michael D. Rice
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: From abstract and introduction: ''A subset S of a metric space X is U- embedded in X if every uniformly continuous real-valued function on S extends to a uniformly continuous real-valued function on X. We consider the uniform extension question and examine the geometry of the problem. In Section 1 we give the definitions and notation which we will need. Section 2 gives some of the results which appear in the literature regarding extension of uniformly continuous functions. In Section 3 we present some general results on U-embedded sets. Section 4 deals with sets which determine boundedness, a concept which is useful in proving various sets are U-embedded. In Section 5 we characterize the U-embedded subsets of the real line. Section 6 gives a characterization of when the union of finitely many lines is U-embedded in \(R^ n\). Section 7 gives a large number of examples of sets in \(R^ n\) and \(R^ 3\) which are designed to indicate the subtle nature of the U-embedding property. Finally, Section 8 deals with U-embedding of the union of finitely many lines in the Lobachevskian plane.''
Mathematics Subject Classification ID: 54C45
Mathematics Subject Classification ID: 54C20
zbMATH DE Number: 3973799
zbMATH Keywords: sets determining boundedness
zbMATH Keywords: Lipschitz region
zbMATH Keywords: uniform extension
zbMATH Keywords: extension of uniformly continuous functions
zbMATH Keywords: U-embedded sets
zbMATH Keywords: real line
reviewed by: Charles E. Aull
MaRDI profile type: Publication
full work available at URL: 0166-8641(86)90006-4
OpenAlex ID: W1983562542
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description: scientific article; zbMATH DE number 3973799