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BORNOLOGIES AND LOCALLY LIPSCHITZ FUNCTIONS

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Garrido, M. Isabel (2014) BORNOLOGIES AND LOCALLY LIPSCHITZ FUNCTIONS. Bulletin of the Australian Mathematical Society, 90 (2). pp. 257-263. ISSN 0004-9727

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Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9332599&fulltextType=RA&fileId=S0004972714000215




Abstract

Let hX, di 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.


Item Type:Article
Uncontrolled Keywords:Lipschitz function; Locally Lipschitz function; Uniformly locally Lipschitz; Function; Lipschitz in the small function, function preserving Cauchy sequences, bornology, totally bounded set; Bourbaki bounded set
Subjects:Sciences > Mathematics > Topology
ID Code:28548
Deposited On:20 Feb 2015 11:38
Last Modified:12 Dec 2018 15:12

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