INFINITE GAMES VIA COVERING PROPERTIES IN IDEAL TOPOLOGICAL SPACES

Abstract

First, we propound a comment about the Meneger (X) game. We show that player TWO has a winning strategy always per contra that player ONE. So, we define a new game, say G(C), by using the same data of the Meneger (X) without any winning strategy for both players in general. In this paper, we are using the concept of ideal topological spaces with its covering prop- erties and I-compactness to introduce infinitely long games like: G(C,I),GD(C,I),GO(C,I) and G(C � ,C). So, we show some results that explain many conditions to make anyone of players have winning strategy. Also, the efficacies of some types of ideals on the strategies for players are studied. Finally, comparisons among player's strategies through the equivalent ideal topological spaces are showed. These have been important topics of research and have been crucial in the development of game theory especially of topological game theory.