- Fundamentals of Contemporary Mathematical Sciences
- Vol: 3 Issue: 2
- Theory of Generalized Compactness in Generalized Topological Spaces: Part II. Countable, Sequential ...
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 : 9 | Download : 5
Publication Date : 2022-07-28
Article Type : Research
Abstract :In a recent paper, a novel class of generalized compact sets (briefly, g-Tg -compact sets) in generalized topological spaces (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 (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 (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