On Directed Baire Spaces

Authors : Renukadevi V, Ravindran THANGAMARİAPPAN

Pages : 156-161

Doi:10.33401/fujma.570126

View : 13 | Download : 7

Publication Date : 2019-12-20

Article Type : Research Paper

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