Generalized ordered spaces with capacities

H. R. Bennett; D. J. Lutzer

doi:10.2140/pjm.1984.112.11

Generalized ordered spaces with capacities

H. R. Bennett, D. J. Lutzer

Mathematics and Statistics

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

4 Scopus citations

Abstract

We show that any GO-space having a capacity in the sense of Sčepin has a G_δ-diagonal and is perfect. In addition, such a space has a σ-discrete dense subset and a dense metrizable subspace, and any GO-space having a capacity and a point-countable base (or having a σ-discrete dense subset and a point-countable base) is metrizable.

Original language	English
Pages (from-to)	11-19
Number of pages	9
Journal	Pacific Journal of Mathematics
Volume	112
Issue number	1
DOIs	https://doi.org/10.2140/pjm.1984.112.11
State	Published - May 1984

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10.2140/pjm.1984.112.11

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abstract = "We show that any GO-space having a capacity in the sense of S{\v c}epin has a Gδ-diagonal and is perfect. In addition, such a space has a σ-discrete dense subset and a dense metrizable subspace, and any GO-space having a capacity and a point-countable base (or having a σ-discrete dense subset and a point-countable base) is metrizable.",

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AB - We show that any GO-space having a capacity in the sense of Sčepin has a Gδ-diagonal and is perfect. In addition, such a space has a σ-discrete dense subset and a dense metrizable subspace, and any GO-space having a capacity and a point-countable base (or having a σ-discrete dense subset and a point-countable base) is metrizable.

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Generalized ordered spaces with capacities

Abstract

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