Daniel T. Soukup, Lajos Soukup
Published 2013-04-01, updated 2014-01-24Version 2
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 Lindel\"of 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 \omega_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.
Comments: 26 pages, revised, submitted to CMUC
A bound for the density of any Hausdorff space
Between countably compact and $ω$-bounded
On the cardinality of Hausdorff spaces and H-closed spaces
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