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

Year 2022, Volume: 3 Issue: 2, 98 - 118, 28.07.2022

Mohammad Irshad Khodabocus , Noor-ul-hacq Sookıa

https://doi.org/10.54974/fcmathsci.1009492

Cited By: 3

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

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