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Media type:
E-Article
Title:
BORNOLOGIES AND LOCALLY LIPSCHITZ FUNCTIONS
Contributor:
BEER, GERALD;
GARRIDO, M. I.
Published:
Cambridge University Press (CUP), 2014
Published in:
Bulletin of the Australian Mathematical Society, 90 (2014) 2, Seite 257-263
Language:
English
DOI:
10.1017/s0004972714000215
ISSN:
0004-9727;
1755-1633
Origination:
Footnote:
Description:
<jats:title>Abstract</jats:title><jats:p>Let<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0004972714000215_inline1" /><jats:tex-math>$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\langle X,d \rangle $</jats:tex-math></jats:alternatives></jats:inline-formula>be a metric space. We characterise the family of subsets of<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0004972714000215_inline2" /><jats:tex-math>$X$</jats:tex-math></jats:alternatives></jats:inline-formula>on which each locally Lipschitz function defined on<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0004972714000215_inline3" /><jats:tex-math>$X$</jats:tex-math></jats:alternatives></jats:inline-formula>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.</jats:p>