Metrization of Fpp-spaces

H. R. Bennett

doi:10.1016/0166-8641(83)90042-1

Metrization of F_pp-spaces

H. R. Bennett

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

A Hausdorff space each subspace of which is a paracompact p-space is an F_pp-space. A space X is a closed hereditary Baire space if each closed subspace of X is a Baire space. Using a delicate theorem of Z. Balogh it is shown that a first-countable F_pp-space that is a closed hereditary Baire space is metrizable.

Original language	English
Pages (from-to)	7-10
Number of pages	4
Journal	Topology and its Applications
Volume	15
Issue number	1
DOIs	https://doi.org/10.1016/0166-8641(83)90042-1
State	Published - Jan 1983

Keywords

54B35, 54D18
Baire space
F-space
metrizable
paracompact p-space

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10.1016/0166-8641(83)90042-1

Cite this

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abstract = "A Hausdorff space each subspace of which is a paracompact p-space is an Fpp-space. A space X is a closed hereditary Baire space if each closed subspace of X is a Baire space. Using a delicate theorem of Z. Balogh it is shown that a first-countable Fpp-space that is a closed hereditary Baire space is metrizable.",

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AB - A Hausdorff space each subspace of which is a paracompact p-space is an Fpp-space. A space X is a closed hereditary Baire space if each closed subspace of X is a Baire space. Using a delicate theorem of Z. Balogh it is shown that a first-countable Fpp-space that is a closed hereditary Baire space is metrizable.

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KW - F-space

KW - metrizable

KW - paracompact p-space

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JO - Topology and its Applications

JF - Topology and its Applications

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Metrization of F_pp-spaces

Abstract

Keywords

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