Other Classes of Generalized Compact Spaces Based on New Generalized ω-Open Sets

The concept of generalized compactness is very useful and essential concept not only in general topology but also in the other advanced branches of pure and applied mathematics. As well one can observe the influence of topological spaces in computer sciences,digital topology, computational topology for geometric and molecular design particle physics, high energy physics, quantum physics and super-string theory. Therefore, new concepts of generalized compact spaces namely, ωδ-ß-compact and nearly ωδ-ß-compact space based on new generalized ω-open sets have been presented in topological spaces. In the process, various essential characterizations related to these kinds of generalized compact spaces have been investigated. Furthermore, the relationships among some kinds of generalized compact spaces have been discussed. As well, some illustrative examples to highlight the realized improvements are supplied.We expect that the discoveries in this article will aid scientists in developing the researches on general topology in order to elevate a general framework for their practical applications in all advanced branches of mathematics and other sciences.