Topological games and productively countably tight spaces

2013/07/30 by Aurichi, Leandro F., Bella, Angelo · 1 citation
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1307.7928

Abstract

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(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 \sone(Ω_x, Ω_x) holds for every x ∈ X. With these results, several other results follow, using some characterizations made by Uspenskii and Scheepers.

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