Abstract
We establish that, for any metrizable space X, if every closed separable subspace of X has the Baire property, then the space X has the Baire property. The same reflection result holds for spaces Cp(X). It is also shown that all closed separable subspaces of Cp(X) are Čech-complete if and only if X is a functionally countable P-space. If A¯ is pseudocomplete for every countable set A⊂Cp(X), then Cp(X) is pseudocomplete. To show that zero-dimensionality does not reflect in closed separable subspaces of metrizable spaces, under Jensen’s Axiom ♢, we give an example of a connected metrizable space M such that A¯ is countable and hence zero-dimensional for every countable set A⊂M.
Published Version
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