Neutrosophic SuperHyper Bi-Topological Spaces: Original Notions and New Insights

Abstract

This manuscript comes as first attempt in building a new type of neutrosophic topological spaces, the aim is to shed the light on a new structure known as the 𝑛 𝑡ℎ -power set 𝑃 𝑛(𝑋) of a set, this new kind of sets enables authors to create and built new topology spaces called Neutrosophic SuperHyper Topological Spaces and Neutrosophic SuperHyper Bi-Topological Spaces , the 𝑛 𝑡ℎ - power sets are the optimal representation for the applications in our real world. In this article, new concepts and theorems related to these new topologies have been discussed, which are pairwise neutrosophic open 𝑛 𝑡ℎ -power set, pairwise neutrosophic closed 𝑛 𝑡ℎ -power set, as well as, the closures and the interiors are defined with their properties. Many of relations for these concepts have been introduced.

Keywords

• neutrosophic superhyper topological spaces
• neutrosophic superhyper bi-topological spaces