DMS Set Theoretic Topology Seminar

Speaker: Vladimir Tkachuk  

Title: Any first countable Lindelof Sigma-space  has a point-countable pi-base.

Abstract: It is a famous deep result of Shapirovsky that any compact space of countable tightness has a point-countable pi-base.  The same result cannot be proved for Lindelof Sigma-spaces because there exist even countable spaces without a countable pi-base. I will show that a Lindelof Sigma-space must have a point-countable pi-base if its tightness and pi-character are countable. This generalizes  the above-mentioned theorem of Shapirovsky because any compact space of countable tightness automatically has countable pi-character. It is worth mentioning that this result is not easy to prove even for first countable sigma-compact spaces.