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Grant Woods - Recent developments in rings of continuous functions



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 $X \times Y$ induced by the family of separately continuous functions on the product $X \times Y$ 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 $\vert C(X \times Y)\vert$.


next up previous
Next: Eduardo Santillan - Topological Up: 3)  Set Theoretic Topology / Previous: E. D. Tymchatyn -
 

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