A Note on Two-Fold Neutrosophic and Fuzzy Topological Space Based on Real Numbers

Rabaa Al-Maita

Department of Mathematics & Statistics, Mutah University, Al-Karak, Jordan

rabaamaita@mutah.edu.jo

Abstract

The objective of this paper is to introduce for the first time the concept of two-fold neutrosophic and fuzzy topological space defined over real numbers, where we combine the two-fold neutrosophic sets with real numbers to get a novel topological space based on them. Also, we present many of its elementary properties and special subsets such as two-fold neutrosophic open sets, two-fold neutrosophic closed sets, and two-fold neutrosophic closure. Many examples and theorems will be provided to clarify the validity of our approach.

Keywords: Two-fold algebra; Two-fold neutrosophic topology; Two-fold neutrosophic open set; Two-fold neutrosophic closed set