Topological games and productively countably tight spaces

摘要

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.