P-SPACES AND INTERMEDIATE RINGS OF CONTINUOUS FUNCTIONS

摘要

A completely regular topological space X is called a P-space if every zero-set in X is open. An intermediate ring is a ring A(X) of real-valued continuous functions on X containing all the bounded continuous functions. In this paper, we find new characterizations of P-spaces X in terms of properties of correspondences between ideals in A(X) and z-filters on X. We also show that some characterizations of P-spaces that are described in terms of properties of C(X) actually characterize C(X) among intermediate rings on X.