-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

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]**J. R. Isbell,*Uniform spaces*, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR**0170323****[LR]**Ronnie Levy and M. D. Rice,*Techniques and examples in 𝑈-embedding*, Topology Appl.**22**(1986), no. 2, 157–174. MR**836323**, 10.1016/0166-8641(86)90006-4**[LR]**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****[LR]**Ronnie Levy and Michael D. Rice,*The approximation and extension of uniformly continuous Banach space valued mappings*, Comment. Math. Univ. Carolin.**24**(1983), no. 2, 251–265. MR**711263**

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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