Geodesic
Partitioning bases of topological spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 4, pp. 537-566

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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 $2^\omega $ and weight $\omega_1$ which admits a point countable base without a partition to two bases.
Classification : 03E35, 54A25, 54A35
Keywords: base; resolvable; partition 
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     title = {Partitioning bases of topological spaces},
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Soukup, Dániel T.; Soukup, Lajos. Partitioning bases of topological spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 4, pp. 537-566. http://geodesic.mathdoc.fr/item/CMUC_2014__55_4_a9/