On a game theoretic cardinality bound

The main purpose of the paper is the proof of a cardinal inequality for a space with points $G_\delta$, obtained with the help of a long version of the Menger game. This result improves a similar one of Scheepers and Tall

Topological games and productively countably tight spaces

The two main results of this work are the following: if a space $X$ is such that player II has a winning strategy in the game \gone(\Omega_x, \Omega_x) for every $x \in X$, then $X$ is productively countably tight. On the other hand, if a space is productively countably tight, then \sone(\Omega_x, \Omega_x) holds for every $x \in X$. With these results, several other results follow, using some characterizations made by Uspenskii and Scheepers

More on the product of pseudo radial spaces

summary:It is proved that the product of two pseudo radial compact spaces is pseudo radial provided that one of them is monolithic