This is an announcement for the paper "Lipschitz-free spaces over metric spaces homeomorphic to the Cantor space" by Petr Hajek, Gilles Lancien and Eva Pernecka.

Abstract: In this note we give an example of a compact metric space which is homeomorphic to the Cantor space and whose Lipschitz-free space fails the approximation property. This answers a question by G. Godefroy. We also prove that there exists an uncountable family of topologically equivalent distances on the Cantor space whose free spaces are pairwise non isomorphic.

Archive classification: math.FA

Submitted from: gilles.lancien@univ-fcomte.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1507.02701

or

http://arXiv.org/abs/1507.02701