TY - JOUR
AU - González-Silva, R. A.
AU - Hrusák, M.
PY - 2013/09/30
Y2 - 2024/08/06
TI - More on ultrafilters and topological games
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 10
IS - 2
SE -
DO - 10.4995/agt.2009.1734
UR - https://polipapers.upv.es/index.php/AGT/article/view/1734
SP - 207-219
AB - <p>Two different open-point games are studied here, the G-game and the Gp-game, defined for each p âˆˆ ωâˆ—. We prove that for each p âˆˆ ωâˆ—, there exists a space in which none of the players of the Gp-game has a winning strategy.</p><p>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.</p><p>We construct a countably compact space in which player II of the Gp-game is the winner, for every p âˆˆ ωâˆ—. 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.</p>
ER -