International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 111-116
The open-open topology for function spaces
Department of Mathematical Sciences, Saint Mary's College of California, Moraga 94575, CA., USA
Received 20 February 1991; Revised 22 January 1992
Copyright © 1993 Kathryn F. Porter. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let and be topological spaces and let . For each , , let . Define the set . Then
is a subbasis for a topology, on , which is called the open-open topology. We compare
with other topologies and discuss its properties. We also show that , on , the collection
of all self-homeomorphisms on , is equivalent to the topology induced on by the Pervin
quasi-uniformity on .