Partitioning bases of topological spaces

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 T_3 Lindelöf topology can be partitioned into two bases while there exists a consistent example of a first countable, 0-dimensional, Hausdorff space of size continuum and weight ω_1 which admits a point countable base without a partition to two bases. Several related results are proved and the paper finishes with a list of open problems.

26 pages, revised, submitted to CMUC