Oxtoby's pseudocompleteness revisited (Q1962096)

\textit{J. C. Oxtoby}'s notion of pseudocompleteness [Fundam. Math. 49, 157-166 (1961; Zbl 0113.16402)] is generalized to nonregular or bitopological spaces; the spaces with the new property are called Oxtoby spaces (they are Baire spaces and, moreover, a space containing a dense Oxtoby subspace is Oxtoby, too). It is showed that every subspace of a product of Oxtoby spaces containing their sigmaproduct, is an Oxtoby space. A general result on preserving pseudocompleteness by \(G_\delta\)-subspaces is proved; as consequences one gets that every \(G_\delta\)-subspace of Sorgenfrey line is pseudocomplete, and any \(G_\delta\)-subspace of a countably subcompact space is a Baire space, which is a result of \textit{M. C. Rayburn} [A question on countably subcompact spaces, Quest. Answers Gen. Topology 5, No. 2, 237-242 (1987)]. A non-Baire \(G_\delta\)-subspace of a pseudocomplete space is presented.