Partitioning bases of topological spaces

summary: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

Partitioning bases of topological spaces

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 T3 Lindelöf topology can be partitioned into two bases while there exists a consistent example of a first-countable, 0-dimensional, Hausdorff space of size 2ω and weight ω1 which admits a point countable base without a partition to two bases