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

Authors : Mohammad Irshad KHODABOCUS, Noorulhacq SOOKIA

Pages : 26-45

Doi:10.54974/fcmathsci.1009467

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Publication Date : 2022-01-30

Article Type : Research Paper

Abstract :In this 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 ); is studied. The study reveals that g-Tg -compactness implies ordinary compactness insert ignore into journalissuearticles values(briefly, Tg -compactness ); in Tg-spaces, and such statement implies its analogue in ordinary topological spaces insert ignore into journalissuearticles values(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