Dániel T. Soukup, Lajos Soukup*
Partitioning bases of topological spaces

Comment.Math.Univ.Carolin. 55,4 (2014) 537-566.

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 $2^\omega $ and weight $\omega_1$ which admits a point countable base without a partition to two bases.

Keywords: base; resolvable; partition
AMS Subject Classification: 54A35 03E35 54A25