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Keywords:
base-base paracompact space; coarse base; Sorgenfrey irrationals; totally imperfect set
Summary:
A topological space $X$ is called base-base paracompact (John E. Porter) if it has an open base $\mathcal B$ such that every base ${\mathcal B' \subseteq \mathcal B}$ has a locally finite subcover $\mathcal C \subseteq \mathcal B'$. 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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