Affiliations: [a] Department of Mathematics, University of Science and Technology Bannu, Pakistan
| [b] Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan
| [c] Department of Humanities and Basic Sciences, MCS, National University of Sciences and Technology, Islamabad, Pakistan
| [d] MIFT-Dipartimento di Scienze Matematichee Informatiche, scienze Fisiche e scienze della Terra, Messina University, Messina, Italy
| [e] Department of Mathematics and Natural Sciences, College of Sciences and Human Studies, Prince Mohammad Bin Fahad University, Khobar, Saudi Arabia
Correspondence:
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Corresponding author. Farkhanda Afzal, Department of Humanities and Basic Sciences, MCS, National University of Sciences and Technology, Islamabad, Pakistan. E-mail: farkhanda@mcs.edu.pk.
Abstract: This paper concern the study of the notions of some new definitions and results. Three new definitions are given namely, neutrosophic soft quad semi-open, neutrosophic soft quad pre-open and neutrosophic soft quad *b open sets in neutrosophic soft quad-topological spaces. Among these one of the interesting neutrosophic soft quad generalized open set known as neutrosophic soft quad pre-open set is chosen then on the basis of this definition some fundamentals are generated. These are including, neutrosophic soft quad interior, neutrosophic soft quad boundary, neutrosophic soft quad exterior and neutrosophic soft quad closer. In continuation, attention has been focused on neutrosophic soft separation axioms which are defined in terms of neutrosophic soft p-open sets with respect to soft points then on the basis of definitions and results given, neutrosophic soft separation axioms are discussed mostly in terms of neutrosophic soft closer of the sets. In addition, some more results are addressed in neutrosophic soft quad-opological spaces with respect to soft points. Stress has been given on the neutrosophic soft quad topological property. Lastly, results on product of neutrosophic soft quad topological spaces, Bolzano-Weierstrass Property, compactness, countably compactness and sequentially compactness are addressed in terms of neutrosophic soft p-open sets in neutrosophic soft quad topological spaces.
Keywords: Neutrosophic soft set, neutrosophic soft points, neutrosophic soft quad-topological space, neutrosophic soft p-open set, set and neutrosophic softp-separation axioms
