More on ultrafilters and topological games

• González-Silva, R.A. ^[1] ; Hrusák, M. ^[2]
  1. [1] Universidad de Guadalajara

     Universidad de Guadalajara

     México

     
  2. [2] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 10, Nº. 2, 2009, págs. 207-219
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.