Theory of Generalized Compactness in Generalized Topological Spaces: Part II. Countable, Sequential and Local Properties

Authors : Mohammad Irshad KHODABOCUS, Noor-ul-hacq SOOKIA

Pages : 98-118

Doi:10.54974/fcmathsci.1009492

View : 10 | Download : 6

Publication Date : 2022-07-28

Article Type : Research Paper

Abstract :In a recent paper, a novel class of generalized compact sets insert ignore into journalissuearticles values(briefly, g-Tg -compact sets); in generalized topological spaces insert ignore into journalissuearticles values(briefly, Tg -spaces); has been studied. In this paper, the concept is further studied and, other derived concepts called countable, sequential, and local generalized compactness insert ignore into journalissuearticles values(countable, sequential, local g-Tg -compactness); in Tg -spaces are also studied relatively. The study reveals that g-Tg -compactness implies local g-Tg -compactness and countable g-Tg-compactness, sequential g-Tg -compactness implies countable g-Tg -compactness and, g-Tg -compactness is a generalized topological property insert ignore into journalissuearticles values(briefly, Tg -property);. Diagrams establish the various relationships amongst these types of g-Tg -compactness presented here and in the literature, and a nice application supports the overall theory.
Keywords : Generalized topological spaces, generalized compactness, countable generalized compactness, sequential generalized compactness, local generalized compactness