Affiliations: [a] Department of Mathematics, Sana’a University, Sana’a, Yemen
| [b] Department of Engineering Mathematics & Physics, Faculty of Engineering & Technology, Future University, Egypt
| [c] Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam Bin Abdulaziz University, Riyadh, Saudi Arabia
| [d] Department of Mathematics, Faculty of Science, Zarqa University, Zarqa, Jordan
| [e] Department of Mathematics, College of Science, University of Duhok, Duhok, Iraq
Abstract: This work introduces weakly soft β-open subsets, a new family of soft-open sets. By this family, we expand a soft topology to a soft structure which is neither supra-soft topology nor infra-soft topology. The connections between this class of soft sets and other celebrated classes via soft topology are examined with some elucidative examples. Also, it is established some relationships under conditions of extended and hyperconnected soft topologies. Furthermore, the interior and closure operators are structured along with weakly soft β-open and weakly soft β-closed sets. Finally, the class of weakly soft β-continuous functions is introduced and its main characterizations are studied. It is investigated the systematic relationships and findings that are lost for this kind of soft continuity as well as it is shown the conditions required to maintain some of these relationships such as full, extended and hyperconnected soft topologies.
