IJPAM: Volume 106, No. 1 (2016)

INFINITE GAMES VIA COVERING PROPERTIES
IN IDEAL TOPOLOGICAL SPACES

A.E. Radwana$^1$, Essam El Seidyb$^2$, R.B. Esmaeelc$^3$
$^{1,2}$Department of Mathematics
Faculty of Science
Ain Shams University
EGYPT
$^3$Department of Mathematics
Ibn Al-Haitham College of Education
Baghdad University
IRAQ


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 $G(\cal{C})$, 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 properties and $I$-compactness to introduce infinitely long games like: $G(\cal{C}, I), G_D(\cal{C}, I), G_O(\cal{C}, I)$ and $G(C^*,\cal{C})$. 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.

Received: September 7, 2015

AMS Subject Classification: 54C08, 54C10, 54D35, 91A05

Key Words and Phrases: ideal, $I$-compact, locally finite, $\tau^*$-open, Meneger game, selection principle, $G(\cal{C}, I), G_D(\cal{C}, I), G_O(\cal{C}, I), G(\cal{C}^*,\cal{C})$ and $G(X, I)$

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DOI: 10.12732/ijpam.v106i1.20 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 1
Pages: 259 - 272


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