On Directed Baire Spaces

Abstract

We study directed Baire spaces and their relevant topological properties. A characterizationof directed Baire spaces is given using point finite family of $G_delta$ −sets. Further, we provethat the product of directed Baire space with a metric hereditarily directed Baire space is adownward-directed Baire space. Finally, it is established that the product of a Baire spacewith a hereditarily metric Volterra space is again a Volterra space.