Alternating Repeated Games via π-Pre-Separation Axioms and Functions
El Seidy, Essam, Radwan, Abdelaziz E., Osman, H. Saber, Tabarak, M. E. · Journal of the Egyptian Mathematical Society · 2024
This paper aims to link topology and game theory by using definitions of π-pre-separation axioms on π-pre-topological spaces. In this paper, we introduce and investigate infinitely long games using the concept of separation axioms on π-pre-topological spaces, specifically π-pre-T0, π-pre-T1, and π-pre-T2. Winning and losing strategies for both players are studied with some examples. In addition, the effects of pre-open, surjective, injective, and pre-continuous functions on both players’ strategies in different kinds of games are also studied.