Some topologically complete spaces

Abstract

If X is either (1) a complete, nonmetrizable Moore space or (2) a certain topologically complete nonmetrizable space that is the closed continuous image of separable complete metric space, then there exists a space Y with the same properties and in which every open set contains a copy of X, and Y satisfies Baire's category theorem. Then, in the first case, Y is a first countable space which has a σ-locally finite network but is not the union of countably many closed metrizable subspaces, and, in the second case, Y is the closed continuous image of a metrizable space which is not such a countable union.