Some soft ideal spaces via infinite games

Abstract

Soft ideal spaces play a significant role in mathematics, particularly in the field of infinite games. They allow mathematicians to establish connections between different areas of mathematics, such as set theory, topology, and game theory. Moreover, soft ideal spaces provide a powerful framework for tackling various problems in analysis, algebra, and geometry. These spaces contribute to the development of mathematical theories, provide a framework for studying, analyzing various properties and operations in infinite game theory, and find applications in various fields including computer science and set theory. Also, these spaces help in characterizing various properties of infinite games, such as determinacy, strategies, and winning conditions. We can gain insights into the behavior of infinite games and develop strategies to optimize outcomes by studying these spaces. This paper aims to use the concept of soft ideal topological spaces to introduce infinitely long games. The study of soft ideal topological space by defining soft ideal separation axioms (τi,i=0,1,2,3,4) is extended followed by some related theorems. Several soft games are explained using soft separation axioms with flowcharts such as ŞĢτ0,χ, ŞĢτ1,χ, ŞĢτ2,χ, ŞĢτ3,χ and ŞĢτ4,χ. Some results explain several conditions to make any player have a winning strategy. Using many figures and propositions to study the relationships between these types of games, with some examples of soft sets.