Computation of the z-radical in C(X)

Abstract

We say that a Tychonoff space X has computable z-radicals if for all ideals a of C(X), the smallest z-ideal containing a is generated as an ideal by all the s circle f, where f is in a and s is a continuous function R --> R with s(-1)(0) = {0}. We show that every cozero set of a compact space has computable z-radicals and that a subset X of R-n has computable z-radicals if and only if X is locally closed.