Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: All articles in the CMB digital archive with keyword continous

 Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2000 (vol 43 pp. 208)

Matoušková, Eva
 Extensions of Continuous and Lipschitz Functions 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 $X$. Keywords:extension, continous, Lipschitz, Banach spaceCategories:54C20, 46B10

© Canadian Mathematical Society, 2015 : https://cms.math.ca/