The Strong Closed Discrete Game on Continuous Functions

Tkachuck introduced the closed discrete game, connecting instances of it on continuous functions to the point-open game on the domain of those functions. Left open was a question of equivalence between the games. Clontz and I made progress on that equivalence, tying the closed discrete game on continuous functions to the finite-open game on the domain. Just this past year, Chiozini modified the closed discrete game (using a subbasis instead of a basis) to define the strong closed discrete game and showed that the strong closed discrete game on continuous functions is strategically equivalent to the point-open game on the domain. Caruvana and I have taken this result and expanded it to include limited information strategies. In this talk we will introduce these games, discuss the different kinds of strategies, explain the link between the games, and dive into the combinatorics that show the games are equivalent for limited information strategies.