A note on point-countability in linearly ordered spaces
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- by Harold R. Bennett PDF
- Proc. Amer. Math. Soc. 28 (1971), 598-606 Request permission
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.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- 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