3:30 - 5:00 M Barr

Epimorphisms in rings of functions

Abstract: If X is a topological space (which we always suppose completely regular), then C(X) (resp. C*(X)) denotes the space of continuous (resp. and bounded) real-valued functions on X. We investigate conditions under which a subspace Y of X induces an epimorphism C(Y) ---> C(X). We also show that C*(Y) ---> C*(X) can be epic iff it is surjective which is true only if Y is closed and, in the normal case that is iff.

Joint work with Bob Raphael and Walter Burgess.