Topologizing homeomorphism groups of rim-compact spaces
by
Anna Di Concilio
Facolta' di Scienze Universita' di Salerno Italia

Let X be a Tychonoff space and H(X) the group of all self-homeomorphisms of X. We give conditions not involving local compactness but rim-compactness that imply the existence on H(X) of a topology which (a) makes it into a topological group, more (b) makes continuous the evaluation function e: (f, x) in H(X)×X --> f(x) in X and further is the minimal one with the properties (a) and (b). When X is rim-compact T₂ and its Freudenthal compactification F(X) is locally connected at any point in F(X)-X, then the topology of uniform convergence w.r.t. the Freudenthal uniformity, also described as the proximal set-open topology generated jointly by the network of all closed sets in X and the Freudenthal proximity of X, is the minimal one with the properties (a) and (b).

Date received: May 15, 2001

Copyright © 2001 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 # cagw-40.