Geodesic
Base-base paracompactness and subsets of the Sorgenfrey line
Mathematica Bohemica, Tome 137 (2012) no. 4, pp. 395-401

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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.
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.
DOI : 10.21136/MB.2012.142995
Classification : 03E15, 26A21, 28A05, 54D20, 54D70, 54F05, 54G20, 54H05
Keywords: base-base paracompact space; coarse base; Sorgenfrey irrationals; totally imperfect set 
Popvassilev, Strashimir G. Base-base paracompactness and subsets of the Sorgenfrey line. Mathematica Bohemica, Tome 137 (2012) no. 4, pp. 395-401. doi: 10.21136/MB.2012.142995
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