Neutrosophic λ-Compactness, λ-Connectedness, and λ-Separation Axioms in Neutrosophic Topological Spaces

Abstract

Real-life structures always include indeterminacy. The Mathematical tool, which is well known indealing with indeterminacy, is neutrosophic. Neutrosophic sets deal with uncertain data. The notion of a neutrosophic set is generally referred to as the generalization of an intuitionistic fuzzy set. In 2025, Shivangi Tyagiand Mridul Kumar Gupta introduced the concept of neutrosophic λ -closed (briefly, N eu λ - closed )sets and N eu λ- open sets and investigated their fundamental properties. In this chapter, we introduce the notions of N eu λ -compact spaces, N eu λ-Lindelof space, countably N eu λ -compact spaces,N eu λ-connected spaces,N eu λ -separated sets, N eu λ-Super- - connected spaces, N eu - Extrem ely- λ disconnected spaces, and N eu - Strongly-λ connected spaces, N eu λ -R egular spaces, strongly N eu λ -R egular spaces, N eu λ -Normal spaces, and strongly N eu λ -Normal spaces by using N eu λ -open sets and N eu λ -closed sets in Neutrosophic topological spaces. We study the basic properties and fundamental characteristics of these spaces in Neurosophic topological spaces