On Directed Baire Spaces

Authors : Renukadevi V, Ravindran Thangamariappan

Pages : 156-161

Doi:10.33401/fujma.570126

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Publication Date : 2019-12-20

Article Type : Research

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.
Keywords : Baire spaces, Dense G$_{delta}-$sets, Directed sets, Nets, p-spaces, Submaximal spaces