$U$-embedded subsets of normed linear spaces
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- by Ronnie Levy and M. D. Rice PDF
- Proc. Amer. Math. Soc. 97 (1986), 727-733 Request permission
Abstract:
A subset $S$ of a metric space $X$ is $U$-embedded in $X$ if every uniformly continuous function $f:S \to R$ extends to a uniformly continuous function $F:X \to R$. Thus $U$-embedding is the uniform analogue of $C$-embedding. The Tietze extension theorem tells us exactly which subsets of metric spaces are $C$-embedded. The uniform analogue would tell us exactly which subsets of metric spaces are $U$-embedded. In this paper, a characterization of $U$-embedded subsets of the Euclidean plane (or any normed linear space) is given.References
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- Ronnie Levy and Michael D. Rice, The extension of equi-uniformly continuous families of mappings, Pacific J. Math. 117 (1985), no. 1, 149–161. MR 777442, DOI 10.2140/pjm.1985.117.149
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 727-733
- MSC: Primary 54E15; Secondary 54C30, 54C45
- DOI: https://doi.org/10.1090/S0002-9939-1986-0845997-3
- MathSciNet review: 845997