Affiliations: [a] Department of Mathematics & Statistics, Riphah International University, Sector I-14, Islamabad, Pakistan
| [b] Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan
| [c] Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Pakistan
| [d] Department of Mathematics, Research Institute for Natural Sciences, Hanyang University Seoul, Republic of Korea
| [e] Department of Data Science, Daejin University, Kyunggi, Korea
Correspondence:
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Corresponding author. Samer Al Ghour, Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan. E-mail: [email protected].
Abstract: This paper concerns the study of the notion of vague soft β-open set and vague soft separation axioms in vague soft topological spaces. By using such notions and that of the vague soft pints, we study the separation axioms βi (with i = 0, 1, 2, 3, 4) in vague soft topological spaces. We give some peculiar examples about them and we prove some relationships between them. The relationship of βi (with i = , 1, 2, 3, 4) spaces with the closer of vague soft β-open set by means of soft points, vague soft countable spaces and their relationship with βi (with i = , 1, 2) spaces by means of soft points are addressed. In continuation, vague soft topological, vague soft inverse topological spaces properties, Bolzano Weirstrass Property(BVP) and its topological characteristics, compact spaces and sequentially compact spaces and their relationship with separation axioms by means soft points are addressed in vague soft topological spaces.
Keywords: Vague soft set (VSS), vague soft point (VSP), vague soft β-open set and vague soft β-separation axioms.
