On Directed Baire Spaces

Abstract

We study directed Baire spaces and their relevant topological properties. A characterization of directed Baire spaces is given using point finite family of $G_\delta-$sets. Further, we prove that the product of directed Baire space with a metric hereditarily directed Baire space is a downward-directed Baire space. Finally, it is established that the product of a Baire space with a hereditarily metric Volterra space is again a Volterra space.