A note on point-countability in linearly ordered spaces

Bennett, Harold R.

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

A note on point-countability in linearly ordered spaces
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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.

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