|GRANT WOODS, Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada|
|Recent developments in rings of continuous functions|
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 induced by the family of separately continuous functions on the product 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 .