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

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