PNPSα-Open Sets and PNPSα-Continuous, Irresolute, Open, Closed and Homeomorphic Mappings in Pentapartitioned Neutrosophic Pythagorean Topological Spaces

Abstract

Pentapartitioned Neutrosophic Pythagorean Topological Spaces (PNP-Top-Spaces) provide an effective mathematical framework for handling uncertainty, indeterminacy, inconsistency, contradiction, and ignorance in complex decision-making and information systems. Motivated by the development of generalized open sets in neutrosophic topology, this paper introduces and studies the concepts of Pentapartitioned Neutrosophic Pythagorean Semi-α-open (PNPSα-open) and PNPSα-closed sets. Fundamental definitions are established, and several basic properties and characterizations of these sets are obtained. The relationships between PNPSα-open sets and existing classes of PNP open, α-open, semi-open, and closed sets are investigated, and inclusion relations among these classes are discussed. Using these newly defined sets, the notions of PNPSα-continuous, PNPSα-irresolute, PNPSα-open, PNPSα-closed, and PNPSα-homeomorphic mappings are introduced. Various properties and characterizations of these mappings are derived by using PNPSα-open and PNPSα-closed sets. Several fundamental properties concerning preservation and composition of mappings are established. In addition, relationships among ordinary continuous mappings, PNPSα-continuous mappings, and PNPSα-irresolute mappings are examined. The behavior of PNPSα-open and PNPSα-closed mappings under composition and homeomorphic equivalence is also investigated.