A non-metrizable compact linearly ordered topological space, every subspace of which has a 𝜎-minimal base

Shi, Wei-Xue

doi:10.1090/S0002-9939-99-04853-4

A non-metrizable compact linearly ordered topological space, every subspace of which has a $\sigma$-minimal base
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by Wei-Xue Shi

Proc. Amer. Math. Soc. 127 (1999), 2783-2791

DOI: https://doi.org/10.1090/S0002-9939-99-04853-4

Published electronically: April 15, 1999

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Abstract:

A collection $\mathcal {D}$ of subsets of a space is minimal if each element of $\mathcal {D}$ contains a point which is not contained in any other element of $\mathcal {D}$. A base of a topological space is $\sigma$-minimal if it can be written as a union of countably many minimal collections. We will construct a compact linearly ordered space $X$ satisfying that $X$ is not metrizable and every subspace of $X$ has a $\sigma$-minimal base for its relative topology. This answers a problem of Bennett and Lutzer in the negative.

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