Bornologies and locally Lipschitz functions

Authors

  • G. Beer California State University, Los Angeles
  • M. I. Garrido

Keywords:

Lipschitz function, locally Lipschitz function, uniformly locally Lipschitz function, Lipschitz in the small functions, bornology, totally bounded set, Bourbaki bounded set

Abstract

Let (X,d) be a metric space. We characterise the family of subsets of X on which each locally Lipschitz function defined on X is bounded, as well as the family of subsets on which each member of two different subfamilies consisting of uniformly locally Lipschitz functions is bounded. It suffices in each case to consider real-valued functions. DOI: 10.1017/S0004972714000215

Author Biography

G. Beer, California State University, Los Angeles

Professor of Mathematics

Published

2014-08-03

Issue

Vol. 90 No. 2 (2014)

Section

Articles
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