# Neutrosophic Soft $\alpha-$Open Set in Neutrosophic Soft Topological Spaces

Document Type : Research Paper

Authors

1 Riphah International University, Sector I-14, Islamabad, Pakistan

2 Department of Mathematics, University of Science and Technology, Bannu, Khyber Pakhtunkhwa, Pakistan

3 Department of Mathematics, Research institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea

4 MIFT-Dipartimento di Dcienze Matematiche e Informatiche, Scienze Fisiche e scienze DellaTerra, Messina University, Messina, Italy

5 School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, P. R. China

Abstract

In this paper, the notion of generalized neutrosophic soft open set (GNSOS) in neutrosophic soft  open set (GNSOS) in neutrosophic soft topological structures relative to neutrosophic soft points is introduced.The concept of generalized neutrosophic soft separation axioms in neutrosophic soft topological spaces with respect to soft points.  Several related properties, structural characteristics have been investigated. Then the convergence of sequence in neutrosophic soft topological space is defined and its uniqueness in generalized neutrosophic soft Hausdorff space (GNSHS) relative to soft points is examined. Neutrosophic monotonous soft function and its characteristics are switched over to different results. Lastly, generalized neutrosophic soft product spaces with respect to crisp points have been addressed.

Keywords