Some Equivalent Topologies on Homeomorphism Groups
by
Kathryn F. Porter
St. Mary's College of California

In 1962, W. J Pervin showed that any topological space, (X, T), is quasi-uniformizable; he described a specific quasi-uniformity (the Pervin quasi-uniformity) that induces the given topology, T, on X. In 1993, K. Porter proved that the topology of quasi-uniform convergence which is induced on the collection of all self-homeomorphisms, H(X), by the Pervin quasi- uniformity, is equivalent to the open-open topology on H(X). We show that in fact all set-open topologies of a certain kind are equivalent to a Pervin-type quasi-uniform convergence on H(X).

Date received: June 1, 1997

Copyright © 1997 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 # caao-18.