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A note on point-countability in linearly ordered spaces


Author: Harold R. Bennett
Journal: Proc. Amer. Math. Soc. 28 (1971), 598-606
MSC: Primary 54.56
DOI: https://doi.org/10.1090/S0002-9939-1971-0275377-2
MathSciNet review: 0275377
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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 $ \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 $ \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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0275377-2
Keywords: Linearly ordered spaces, point-countable base, $ \sigma $-point-finite base, quasi-developable space
Article copyright: © Copyright 1971 American Mathematical Society

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