A metrization theorem

Phillip Zenor

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Base-base paracompactness and subsets of the Sorgenfrey line

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A topological space $X$ is called base-base paracompact (John E. Porter) if it has an open base $ℬ$ such that every base $ℬ^{'} \subseteq ℬ$ has a locally finite subcover $𝒞 \subseteq ℬ^{'}$ . It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.

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