Neutrosophic Generalized Regular Star Compact, Connected, Regular and Normal 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 2022, S. Pious Missier, A. Anusuya and J. Martina Jency introduced and studied the concepts of Neutrosophic generalized regular star closed   eu closed *-N gr sets and Neutrosic generalized regular star   eu open *-N gr sets in Neutrosophic topological spaces and studied some of their properties and characterizations as well as analyzed the relationships between these newly introduced sets and the already existing neutrosophic sets. In this paper, we introduce the notions of eu compact spaces, *-N gr eu Lindelof *-N gr space, countably eu compact *-N gr spaces, eu connected *-N gr spaces, eu spaces, strongly egular eu *-NR gr spaces, eu *-N gr N orm al spaces, and strongly eu *-N gr N orm al spaces by using open eu *-N gr sets and closed eu *-N gr sets in Neutrosophic topological spaces. We study the basic properties and fundamental characteristics of these spaces in Neutrosophic topological spaces.