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2019•Fundamental Journal of Mathematics and ApplicationsOpen access

On Directed Baire Spaces

V. Renukadevi, Ravindran THANGAMARİAPPAN

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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.

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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.

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Available 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.

Key concepts: Baire space, Baire measure, Baire category theorem, Mathematics, Complete metric space, Metric space, Space (punctuation), Product (mathematics)

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