On the space of Lipschitz homeomorphisms of a compact polyhedron

Abstract

Let X be a positive dimensional compact Euclidean polyhedron. Let H(X), HUP{X) and H PL (X) be respectively the space of homeomorphisms, the space of Lipschitz homeomorphisms and the space of piecewise-linear homeomorphisms of X onto itself. In this paper, we establish a homeomorphism taking the