Fields institute,Room 210
Speaker: Daniel Soukup
Title: Partitioning bases of topological spaces
Abstract: The purpose of this talk is to investigate whether an arbitrary base for a dense in itself topological space can be partitioned into two bases; these spaces will be called base resolvable. First, we review positive results, i.e. that several classes of spaces are base resolvable: metric spaces and left-or right separated spaces. Furthermore, every T_3 (locally) Lindelöf space is base resolvable. Second, we aim to outline the construction of a non base resolvable space; this is done by isolating a new partition property of partially ordered sets. Our strongest result in this direction is that, consistently, there is a 0-dimensional, 1st countable Hausdorff space of weight $\omega_1$ and size continuum which is non base resolvable.
joint work with L. Soukup.