Tuesday, February 4 from 2 to 3pm

*Room*: Mathematics 136

*Speaker*: Rodrigo Roque Dias

*Title*: The point-open game in products

*Abstract*: The point-open game was introduced independently by R. Telgársky (1975) and F. Galvin (1978). In Telgársky’s paper, he asks whether the property “player One has a winning strategy in the point-open game” is finitely productive. In this talk we will answer Telgársky’s question in the affirmative and discuss variations of this result in the context of Rothberger spaces; in particular, we will show that a space in which player One has a winning strategy in the point-open game is productively Rothberger. If time permits, we will also discuss how the proofs of the above results can be adapted to the context of Menger spaces and the Menger game.