Pseudo-completeness and the product of baire spaces

Abstract

The class of pseudo-complete spaces defined by Oxtoby is one of the largest known classes E with the property that any member of E is a Baire space and & is closed under arbitrary products. Furthermore, all of the classical examples of Baire spaces belong to In this paper it is proved that if Je and if X ∈Y is any (quasi-regular) Baire space, then X × Y is a Baire space. The proof is based on the notion of A-embedding which makes it possible to recognize whether a dense subspace of a Baire space is a Baire space in its relative topology. Finally, examples are presented which relate pseudo-completeness to several other types of completeness. © 1973 Pacific Journal of Mathematics All Rights Reserved.