Partitioning bases of topological spaces

Soukup, Dániel Tamás and Soukup, Lajos (2014) Partitioning bases of topological spaces. COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 55 (4). pp. 537-566. ISSN 0010-2628

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Abstract

We investigate whether an arbitrary base for a dense-in-itself topological space can be partitioned into two bases. We prove that every base for a T3 Lindelöf topology can be partitioned into two bases while there exists a consistent example of a first-countable, 0-dimensional, Hausdorff space of size 2ω and weight ω1 which admits a point countable base without a partition to two bases.

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