Weakly Generalized β- Continuous Mapping in Neutrosophic Bitopological Spaces

Abstract

This paper explores the notion of β-continuity in neutrosophic bitopological spaces, a specialized area of mathematics that extends classical topological concepts to handle indeterminate or uncertain information. The study begins with the introduction of τ₁τ₂ semi-closed sets and τ₁τ₂-weakly continuous functions, which are fundamental building blocks. Key results include Proposition 2.1.3, which characterizes τ₁τ₂-weakly β-continuous mappings in terms of pre-images and β-interiors of open sets in the codomain space. Propositions 2.1.4 and 2.1.5 establish equivalent conditions for τ₁τ₂-weakly β-continuous functions involving pre-images, closures, and regular closed sets. Propositions 2.1.6 and 2.1.7 provide alternative characterizations of τ₁τ₂-weakly β-continuous functions, revealing connections with β-interiors and pre-image relationships. These findings contribute to the understanding of topological properties in neutrosophic bitopological spaces, offering valuable insights for further research in this intricate field.