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 G 1 ( Ω x , Ω x ) for every x ∈ X , then X is productively countably tight. On the other hand, if a space is productively countably tight, then S 1 ( Ω x , Ω x ) holds for every x ∈ X . With these results, several other results follow, using some characterizations made by Uspenskii and Scheepers.