More on ultrafilters and topological games


  • R. A. González-Silva Universidad de Guadalajara
  • M. Hrusák Universidad Nacional Autónoma de México



open-point game, ultrafilter, G-space, Gp-space, countably compact


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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Author Biographies

R. A. González-Silva, Universidad de Guadalajara

Departamento de Ciencias Exactas y Tecnológicas

M. Hrusák, Universidad Nacional Autónoma de México

Instituto de Matemáticas


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How to Cite

R. A. González-Silva and M. Hrusák, “More on ultrafilters and topological games”, Appl. Gen. Topol., vol. 10, no. 2, pp. 207–219, Sep. 2013.