Set Theoretic Topology Seminar

Speaker: Steven Clontz ('15), University of North Carolina at Charlotte

Steven will talk about a couple of topological games he has been considering. 

Abstract: A space $X$ has selective separability if given $D_n$ dense in $X$ for $n<\omega$, there exist finite subsets $E_n\subseteq D_n$ such that $\bigcup_{n<\omega} E_n$ is a dense subset of $X$. Barman and Dow first studied the natural game theoretic analogue, giving a positive solution for countable spaces to a question of Gruenhage: may a perfect information strategy in this game always be improved to a Markov information (latest move and round number) strategy? Clontz will discuss results due to Arhangel'skii, Barman, and Dow connecting this game to the Menger game and a game concerning countable fan tightness, and how these results may shed some light on the general question.

FOR PDF, click here

For stream, click here