Theory of Generalized Sets in Generalized Topological Spaces

Authors : Mohammad Irshad Khodabocus, Noor-ul-hacq Sookia

Pages : 18-38

Doi:10.53570/jnt.896345

View : 18 | Download : 13

Publication Date : 2021-09-30

Article Type : Research

Abstract :Several specific types of generalized sets (briefly, g-T_g-sets in generalized topological spaces (briefly, T_g-spaces have been defined and investigated for various purposes from time to time in the literature of T_g-spaces. Our recent research in the field of a new class of g-T_g-sets in T_g-spaces is reported herein as a starting point for more generalized classes. It is shown that the class of g-T_g-sets is a superclass of those whose elements are called open, closed, semi-open, semi-closed, pre-open, pre-closed, semi-pre-open, and semi-pre-closed sets in a T_g-space. A subclass of the T_g-subspace corresponds to the class of g-T_g-sets of a T_g-space. A class of g-T_g-sets of the Cartesian product of these T_g-spaces corresponds to the Cartesian product of a finite number of classes of g-T_g-sets, each of which belongs to a T_g-space. Diagrams establish the various relationships amongst the classes presented here and in the literature, and an ad hoc application supports the overall theory.
Keywords : Generalized topology, Generalized topological space, Generalized operations, Generalized open sets, Generalized closed sets