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

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 ) inTg-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.