International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 299-302

The regular open-open topology for function spaces

Kathryn F. Porter

Department of Mathematical Sciences, Saint Mary's College of California, Moraga 94575, CA, USA

Received 6 July 1993; Revised 13 March 1995

Copyright © 1996 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.


The regular open-open topology, Troo, is introduced, its properties for spaces of continuous functions are discussed, and Troo is compared to Too, the open-open topology. It is then shown that Troo on H(X), the collection of all self-homeomorphisms on a topological space, (X,T), is equivalent to the topology induced on H(X) by a specific quasi-uniformity on X, when X is a semi-regular space.