More on ultrafilters and topological games

R.A. González-Silva, M. Hrusák

Abstract

Two different open-point games are studied  here,  the G-game and the Gp-game, defined for each p ∈ ω∗. We prove that for each p ∈ ω∗, there exists a space in  which none of  the players of  the Gp-game has a winning  strategy.

Nevertheless a result of P. Nyikos, essentially shows that it is consistent, that there exists a countable space in which all these games are undetermined.

We construct a countably compact space in which player II of the Gp-game is the winner, for every p ∈ ω∗. With the same technique of construction we built a countably compact space X, such that in X ×X player II of the G-game is the winner. Our last result is to construct ω1-many countably compact spaces, with player I of the G-game as a winner in any countable product of them, but player II is the winner in the product of all of them in the G-game.


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Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt