Tetra Neutrosophic Alpha Star Generalized #Ψ Mappings in TetraNeutrosophic Topological Spaces

Abstract

In 2026, R. Radha, R. Princy, and Arokia Pratheesha S. V. introduced Tetra Neutrosophic Sets and investigated their fundamental properties. In 2024, S. Pooja, M. Vignashwaren, and L. Vidyarani introduced the concept of  g -closed * # sets in topological spaces. In the same year, they further investigated  g -continuous * # and irresolute maps. Motivated by these developments, we introduce the concept of Tetra Neutrosophic closed - g * # sets in Tetra Neutrosophic topological spaces and investigate their fundamental properties. Based on this new class of generalized closed sets, we introduce Tetra Neutrosophic  g -continuous, * #  g -irresolute, * # open, - g* # and closed - g* # mappings. Their basic properties and characterizations are established. Furthermore, Tetra Neutrosophic  g -homeomorphisms * # are introduced, and some of their fundamental properties are investigated. The obtained results extend the theory of generalized mappings to the Tetra Neutrosophic topological setting and provide a systematic framework for studying generalized transformations between TN-Top-Spaces.