Neutrosophic Generalized Semi Alpha Star Compact, Connected, Regular and Normal Spaces in Topological Spaces

Abstract

Real-life structures always include indeterminacy. The Mathematical tool which is well known in dealing with indeterminacy is Neutrosophic. Smarandache proposed the approach of Neutrosophic sets. Neutrosophic sets deal with uncertain data. The notion of Neutrosophic set is generally referred to as the generalization of intuitionistic fuzzy set. In 2021, P. Anbarasi Rodrigo and S. Maheswari introduced new concepts of Neutrosophic closed sets namely Neutrosophic generalized semi alpha star closed   eu briefly N gsα*-closed sets and eu N gsα*-open sets as well as eu N gsα*-continuity in Neutrosophic topological spaces and studied their some properties. In this chapter, we introduce the notions of eu N gsα*-compact spaces, eu N gsα*-Lindelof space, countably eu N gsα*-compact spaces, eu N gsα*-connected spaces, eu N gsα*-cseparated sets, eu N -Super-gsα*-connected spaces, eu N -Extrem ely-gsα*-disconnected spaces, and eu N -Strongly-gsα*-connected spaces, eu N gsα*-R egular spaces, strongly eu N gsα*-R egular spaces, eu N gsα*-Normal spaces, and strongly eu N gsα*-Normal spaces by using eu N gsα*-open sets and eu N gsα*-closed sets in Neutrosophic topological spaces. We study their basic properties and fundaments characteristics of these spaces in Neurosophic topological spaces.