A note on point-countability in linearly ordered spaces

Harold R. Bennett

doi:10.1090/S0002-9939-1971-0275377-2

A note on point-countability in linearly ordered spaces

Harold R. Bennett

Mathematics and Statistics

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

20 Scopus citations

Abstract

In this note linearly ordered topological spaces (abbreviated LOTS) with a point-countable base are examined. It is shown that a LOTS is quasi-developable if and only if it has a σ-point-finite base and a LOTS with a point-countable base is paracompact. An example of a LOTS with a point-countable base that does not have a σ-point-finite base is given. Conditions are given for the metrizability of a LOTS with a point-countable base and it is shown that a connected LOTS with a point-countable base is homeomorphic to a connected subset of the real line.

Original language	English
Pages (from-to)	598-606
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	28
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1971-0275377-2
State	Published - May 1971

Keywords

Linearly ordered spaces
Point-countable base
Quasi-developable space
σ-Pointfinite base

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10.1090/S0002-9939-1971-0275377-2

Cite this

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AB - In this note linearly ordered topological spaces (abbreviated LOTS) with a point-countable base are examined. It is shown that a LOTS is quasi-developable if and only if it has a σ-point-finite base and a LOTS with a point-countable base is paracompact. An example of a LOTS with a point-countable base that does not have a σ-point-finite base is given. Conditions are given for the metrizability of a LOTS with a point-countable base and it is shown that a connected LOTS with a point-countable base is homeomorphic to a connected subset of the real line.

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A note on point-countability in linearly ordered spaces

Abstract

Keywords

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