DMS Set Theoretic Topology Seminar

Speaker: Professor Vladimir Tkachuk

Title: Lindelof property is discretely reflexive in spaces of countable tightness.

Abstract: After finishing the construction of the example of a crowded countable space which is not weakly discretely generated,  we will start the proof of discrete reflexivity of the Lindelof property in spaces of countable tightness. In other words, we will prove that if \(X\) is a space of countable tightness and the closure of every discrete subspace of \(X\) is Lindelof, then \(X\) itself is Lindelof. This non-trivial theorem of Arhangel'skii is not easy to prove even for first countable spaces.