In this paper we show when a bijection on a set X can be made either an isometry or an expansive map with respect to a non-discrete metric on X. As a corollary we obtain that any bijection on an infinite set can be made biLipschitz by a non-discrete metric.
On bijections, isometries and expansive maps / LE DONNE, Attilio; Fedeli, Alessandro. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - 23:1(2016), pp. 57-61.
On bijections, isometries and expansive maps
Attilio Le donne;
2016
Abstract
In this paper we show when a bijection on a set X can be made either an isometry or an expansive map with respect to a non-discrete metric on X. As a corollary we obtain that any bijection on an infinite set can be made biLipschitz by a non-discrete metric.File allegati a questo prodotto
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