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arXiv · 1304.0472

Partitioning bases of topological spaces

Daniel T. Soukup·Lajos Soukup
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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 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.

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Daniel T. Soukup, Lajos Soukup. 2013-04-01. Partitioning bases of topological spaces. https://arxiv.org/abs/1304.0472

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