Once again on topological spaces containing a dense completely metrizable subset (Q6142396)

The author present characterizations of regular spaces that contain a dense completely metrizable subspace. Each states that a multi-valued map from a Baire space to the space \(X\) under consideration admits a continuous selection on a dense \(G_\delta\)-subset of its domain. The paper concludes with some applications, such as versions of the Closed Graph and Open Mapping theorems for completely metrizable topological vector spaces.