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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