A note on point-countability in linearly ordered spaces-Reference-Cited by-同舟云学术

A note on point-countability in linearly ordered spaces

Published:1971 Issue:2 Volume:28 Page:598-606
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Bennett Harold R.

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 \sigma -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 \sigma -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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1971-028-02/S0002-9939-1971-0275377-2/S0002-9939-1971-0275377-2.pdf

Reference24 articles.

1. Some results in the theory of topological spaces obtained within the last twenty-five years;Aleksandrov, P. S.;Russian Math. Surveys,1960

2. On a class of spaces containing all metric and all locally bicompact spaces;Arhangel′skiĭ, A.;Dokl. Akad. Nauk SSSR,1963

3. Some metrization theorems;Arhangel′skiĭ, A. V.;Uspehi Mat. Nauk,1963

4. Topological spaces with a 𝜎-point finite base;Aull, C. E.;Proc. Amer. Math. Soc.,1971

5. H. R. Bennett, Quasi-developable spaces, Dissertation, Arizona State University, Tempe, Ariz., 1967.

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