BORNOLOGIES AND LOCALLY LIPSCHITZ FUNCTIONS
2014 ◽
Vol 90
(2)
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pp. 257-263
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Keyword(s):
AbstractLet$\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 $be a metric space. We characterise the family of subsets of$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.
1993 ◽
Vol 47
(2)
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pp. 205-212
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Keyword(s):
2015 ◽
Vol 36
(3)
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pp. 1167-1192
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1995 ◽
Vol 87
(3)
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pp. 579-594
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Keyword(s):
2003 ◽
Vol 45
(1)
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pp. 131-141
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2001 ◽
Vol 28
(4)
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pp. 193-198
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2003 ◽
Vol 2003
(1)
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pp. 19-31
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2015 ◽
Vol 368
(7)
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pp. 4685-4730
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Keyword(s):