Baire and Volterra spaces

Gruenhage, Gary; Lutzer, David

doi:10.1090/S0002-9939-00-05346-6

Baire and Volterra spaces
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by Gary Gruenhage and David Lutzer PDF

Proc. Amer. Math. Soc. 128 (2000), 3115-3124 Request permission

Abstract:

In this paper we describe broad classes of spaces for which the Baire space property is equivalent to the assertion that any two dense $G_{\delta }$-sets have dense intersection. We also provide examples of spaces where the equivalence does not hold. Finally, our techniques provide an easy proof of a new internal characterization of perfectly meager subspaces of $[0,1]$ and characterize metric spaces that are always of first category.

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