Fuzzy Topological Games and Related Topics

Abstract

The main purpose of study is to extend the concept of the topological game G(K, X) and some other kinds of games into fuzzy topological games and to obtain some results regarding them. Owing to the fact that topological games have plenty of applications in covering properties, it made an attempt to explore some inter relations of games and covering properties in fuzzy topological spaces. Even though the main focus is on fuzzy para-meta compact spaces and closure preserving shading families, some brief sketches regarding fuzzy P-spaces and Shading Dimension is also provided. In a topological game players choose some objects related to the topological structure of a space such as points, closed subsets, open covers etc. More over the condition on a play to be winning for a player may also include topological notions such as closure, convergence, etc. It turns out that topological games are related to the Baire property, Baire spaces, Completeness properties, Convergence properties, Separation properties, Covering and Base properties, Continuous images, Suslin sets, Singular spaces etc.