Recent Developments in Rings of Continuous Functions
by
Grant Woods
University of Manitoba

In 1960 Gillman and Jerison's text "Rings of Continuous Functions", one of the most influential books on general topology ever written, was published. Thirty-eight years later researchers are still investigating the structure of the ring C(X) of continuous real-valued functions defined on a Tychonoff topological space. In this talk I review recent work by myself and others on three different topics concerning C(X): (1) The weak topology on the set X x Y induced by the family of separately continuous functions on the product X x Y of Tychonoff spaces X and Y. (2) Regular rings of quotients of C(X), particularly its epimorphic hull. (3) The relationship among the cardinal numbers |C(X)|, |C(Y)|, and |C(X x Y)|.

Date received: September 23, 1998

Copyright © 1998 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 # cabr-03.