MATHEMATICA BOHEMICA, Vol. 137, No. 4, pp. 395-401, 2012

# Base-base paracompactness and subsets of the Sorgenfrey line

## Strashimir G. Popvassilev

Strashimir G. Popvassilev, The City College of New York, 160 Convent Avenue, New York, NY 10031, U.S.A., e-mail: spopvassilev@ccny.cuny.edu, strash.pop@gmail.com

Abstract: 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.

Keywords: base-base paracompact space, coarse base, Sorgenfrey irrationals, totally imperfect set

Classification (MSC 2010): 54D20, 54D70, 54F05, 54G20, 54H05, 03E15, 26A21, 28A05

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