Generalized s-Topologies
by
Sherif El-Helaly
The Catholic University of America

Let A be a topological algebra with topology \tau. A subset U subset or equal A is said to be an \alpha-set (where \alpha is a positive number) provided that x², y² in U implies xy in \alphaU. We say that \tau is a generalized s-topology (and A is a generalized s-algebra) if \tau has a 0-neighborhood base consisting of \alpha-sets (possibly with dffferent \alpha's). We discuss the consequences of the presence of a generalized s-topology on A, particularly those which are related to problems of unconditional convergence. Special attention will be given to the case when (A, \tau) is complete and metrizable.

Date received: April 12, 1996

Copyright © 1996 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 # caae-19.