The class of pseudo-complete
spaces defined by Oxtoby is one of the largest known classes 𝒞 with the property that
any member of 𝒞 is a Baire space and 𝒞 is closed under arbitrary products.
Furthermore, all of the classical examples of Baire spaces belong to 𝒞. In
this paper it is proved that if x ∈𝒞 and if 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.
