Geodesic
Extensions of Continuous and Lipschitz Functions
Canadian mathematical bulletin, Tome 43 (2000) no. 2, pp. 208-217

Voir la notice de l'article provenant de la source Cambridge University Press

We show a result slightly more general than the following. Let $K$ be a compact Hausdorff space, $F$ a closed subset of $K$ , and $d$ a lower semi-continuous metric on $K$ . Then each continuous function $f$ on $F$ which is Lipschitz in $d$ admits a continuous extension on $K$ which is Lipschitz in $d$ . The extension has the same supremum norm and the same Lipschitz constant.As a corollary we get that a Banach space $X$ is reflexive if and only if each bounded, weakly continuous and norm Lipschitz function defined on a weakly closed subset of $X$ admits a weakly continuous, norm Lipschitz extension defined on the entire space $X$ .
DOI : 10.4153/CMB-2000-028-0
Mots-clés : 54C20, 46B10, extension, continuous, Lipschitz, Banach space 
Matoušková, Eva. Extensions of Continuous and Lipschitz Functions. Canadian mathematical bulletin, Tome 43 (2000) no. 2, pp. 208-217. doi: 10.4153/CMB-2000-028-0
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