Baire and Volterra spaces

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.