The Topological Weak Rohlin Property and Topological Entropy
by
Eli Glasner
Tel Aviv University
Coauthors: B. Weiss

For a compact metric space X let G=G(X) denote the group of self homeomorphisms with the topology of uniform convergence of homeomorphisms and their inverses. The group G acts on itself by conjugation and we say that X satisfies the topological weak Rholin property if this action has dense orbits. We show that both the Hilbert cube and the Cantor set satisfy this property. We also show that zero entropy is generic for homeomorphisms of the Cantor set, whereas it is infinite entropy which is generic for homeomorphisms of the Hilbert cube. Other spaces are briefly discussed. This is a joint work with B Weiss.

Date received: July 27, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadp-02.