Baire spaces, G_δ’s, and directed complete spaces - Fleissner, William; Yengulalp, Lynne (Topology Proceedings, 2021)
We discuss the proof of the Baire Category Theorem. We review Cech-completeness, pseudocompleteness, and various forms of α-favorability. We present recent results about subcompactness, directed completeness, the Banach-Mazur game, and the strong Choquet game. A recurring theme is whether a completeness property is inherited by G_δ subspaces. We prove that the class of regular directed complete spaces is exactly the class of G_δ subspaces of subcompact spaces.