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Lipschitz-type functions on metric spaces


Garrido, M. Isabel and Jaramillo Aguado, Jesús Ángel (2008) Lipschitz-type functions on metric spaces. Journal of Mathematical Analysis and Applications, 340 (1). pp. 282-290. ISSN 0022-247X

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In order to find metric spaces X for which the algebra Lip*(X) of bounded Lipschitz functions on X determines the Lipschitz structure of X, we introduce the class of small-determined spaces. We show that this class includes precompact and quasi-convex metric spaces. We obtain several metric characterizations of this property, as well as some other characterizations given in terms of the uniform approximation and the extension of uniformly continuous functions. In particular we show that X is small-determined if and only if every uniformly continuous real function on X can be uniformly approximated by Lipschitz functions.

Item Type:Article
Uncontrolled Keywords:Lipschitz functions; Banach–Stone theorem; Uniform approximation
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Topology
ID Code:15504

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