Theory of Generalized Compactness in Generalized Topological Spaces: Part I. Basic Properties

Mohammad Irshad Khodabocus; Noor-ul-hacq Sookıa

doi:10.54974/fcmathsci.1009467

Research Article

Theory of Generalized Compactness in Generalized Topological Spaces: Part I. Basic Properties

Year 2022, Volume: 3 Issue: 1, 26 - 45, 30.01.2022

Mohammad Irshad Khodabocus , Noor-ul-hacq Sookıa

https://doi.org/10.54974/fcmathsci.1009467

Cited By: 4

Abstract

In this paper, a novel class of generalized compact sets (brieﬂy, g-Tg-compact sets ) in generalized topological spaces (brieﬂy,
Tg-spaces ) is studied. The study reveals that g-Tg -compactness implies ordinary compactness (brieﬂy, Tg -compactness ) in
Tg-spaces, and such statement implies its analogue in ordinary topological spaces (brieﬂy, T -spaces ). Diagrams establish the various relationships amongst these types of g-Tg -compactness presented here and in relation to other types of g-T -compactness
in T-spaces presented in the literature of Tg -spaces, and a nice application supports the overall theory.

Keywords

Generalized topology, generalized topological spaces, generalized sets, generalized compactness

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