Propriétés locales de l'espace des homéomorphismes de Brouwer

Abstract

We consider in this paper the space of all orientation preserving and fixed point free homeomorphisms of the plane, endowed with the compact-open topology. Our main theorem asserts that this space is locally contractible. Then we give a new proof of the path connectedness. Finally, it is shown that the inclusion of this space into the space of all orientation preserving planar homeomorphisms induces the trivial map on the fundamental groups.