University of MaraghehSahand Communications in Mathematical Analysis2322-5807Articles in Press20230912$f_{\delta}$-Open Sets in Fine Topological Spaces70756910.22130/scma.2023.1989720.1256ENP. L.PowarDepartment of Mathematics and Computer Science, R.D. University, Jabalpur, India.0000-0002-6332-9386BaravanAsaadDepartment of Computer Science, College of Science, Cihan University-Duhok, Iraq.Department of Mathematics, Faculty of Science, University of Zakho, Iraq.0000-0002-2049-2044J. K.MaitraDepartment of Mathematics and Computer Science, R.D. University, Jabalpur, India.RamratanKushwahaDepartment of Mathematics and Computer Science, R.D. University, Jabalpur, India.0000-0001-9081-593XJournal Article20230215In this paper, the concept of $\delta$-cluster point on a set which belongs to the collection of fine open sets generated by the topology $\tau$ on $X$ has been introduced. Using this definition, the idea of $f_\delta$-open sets is initiated and certain properties of these sets have also been studied. On the basis of separation axioms defined over fine topological space, certain types of $f_\delta$-separation axioms on fine space have also been defined, along with some illustrative examples.