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.

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