Necessary and Sufficient Conditions for a Stability of the Concepts of Stable Interior and Stable Exterior via Neutrosophic Crisp Sets

Doaa Nihad Tomma^1,*, L. A. A. Al-Swidi ²

^{1, 2}Department of Mathematics, College of Education for Pure Science, University of Babylon, Hillah, Iraq.

Emails: doaa.tuama.pure526@student.uobabylon.edu.iq; pure.leal.abd@uobabylon.edu.iq

*Correspondence: doaa.tuama.pure526@student.uobabylon.edu.iq

Abstract

The general direction for generating any stable neutrosophic crisp topology is through base or the stable neutrosophic crisp interior concept, which is closed in the finite intersection process and not closed in the union process, likewise the stable neutrosophic crisp exterior is closed in the finite union process but not closed in finite intersection. Our research deals with finding necessary and sufficient condition for the finite union and finite intersection to be closed respectively using the concept of confused crisp sets.

Keywords: Stable Neutrosophic Crisp Topological Spaces; Stable Neutrosophic Crisp Interior Set; Stable Neutrosophic Crisp Exterior Set; Confused Crisp Set.