@article{article_1009467, title={Theory of Generalized Compactness in Generalized Topological Spaces: Part I. Basic Properties}, journal={Fundamentals of Contemporary Mathematical Sciences}, volume={3}, pages={26–45}, year={2022}, DOI={10.54974/fcmathsci.1009467}, author={Khodabocus, Mohammad Irshad and Sookıa, Noor-ul-hacq}, keywords={Generalized topology, generalized topological spaces, generalized sets, generalized compactness}, 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.}, number={1}, publisher={Mustafa UÇKUN}