-embedded subsets of normed linear spaces
Authors:
Ronnie Levy and M. D. Rice
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
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Abstract | References | Similar Articles | Additional Information
Abstract: A subset of a metric space
is
-embedded in
if every uniformly continuous function
extends to a uniformly continuous function
. Thus
-embedding is the uniform analogue of
-embedding. The Tietze extension theorem tells us exactly which subsets of metric spaces are
-embedded. The uniform analogue would tell us exactly which subsets of metric spaces are
-embedded. In this paper, a characterization of
-embedded subsets of the Euclidean plane (or any normed linear space) is given.
- [I] John Isbell, Uniform spaces, Math. Surveys, no. 12, Amer. Math. Soc., Providence, R. I., 1964. MR 0170323 (30:561)
- [LR
] Ronnie Levy and M. D. Rice, Techniques and examples in
-embedding, Topology Appl. (to appear). MR 836323 (87m:54046)
- [LR
] -, The extension of equi-uniformly continuous families of mappings, Pacific J. Math. 12 (1985), 149-161. MR 777442 (86f:54026)
- [LR
] -, The approximation and extension of uniformly continuous Banach space valued mappings, Comment. Math. Univ. Carolin. 24 (1983), 251-265. MR 711263 (84k:26003)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1986-0845997-3
Keywords:
-embedding,
Lipschitz for large distances
Article copyright:
© Copyright 1986
American Mathematical Society