Cardinal Generalization of Generalized Topological Spaces

Abstract

A cardinal generalization of generalized topological spaces called \(\gamma\)-generalized topological spaces are introduced and various topological concepts and properties on this generalized space are defined and studied. Examples of \(\gamma\)-generalized topological spaces which are not generalized topological spaces are cited. Two special sets on \(\gamma\)-generalized topological spaces are defined and their various properties are also investigated. The topological structure formed by these sets is examined.