A Study on Filters in Topological Spaces

Dheargham Ali Abdulsada^1,*, Audy Hatim Saheb², Rasheed Al-Salih¹, Mohammed Hadi Lafta¹

¹Department of Mathematics, College of Education, University of Sumer, Iraq

²Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Iraq

Emails: d.ali@uos.edu.iq; pure.aday.saheb@uobabylon.edu.iq; basheerreh79@gmail.com; mohamnedhadi@yahoo.com

Abstract

In this research, we introduce and develop new concepts in the field of Neutrosophic Topology (NCT). Particularly our study is focusing on the filter and its properties. Also, we present the properties of convergence of -filter, a specialized filter that incorporates neutrosophic values, providing a robust approach to handle uncertainty in topological spaces. Additionally, we explore the concept of adherent points in neutrosophic crisp triple topological spaces, offering a new perspective on the study of these spaces. Moreover, our findings contribute to expanding the understanding and application of neutrosophic theories in topology that will provide a solid foundation for future research in this area. Furthermore, this work opens new avenues for the study of topological spaces under uncertainty, with potential Applications in various domains, including data analysis, decision-making, and artificial intelligence, among others.

Keywords: Set; Point; Filter; Ultra Filter