\(f_\delta\)-open sets in fine topological spaces. (English) Zbl 07807041
Summary: In 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.
MSC:
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 54A10 | Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) |
| 54C05 | Continuous maps |
| 54C10 | Special maps on topological spaces (open, closed, perfect, etc.) |
| 54D10 | Lower separation axioms (\(T_0\)–\(T_3\), etc.) |
Keywords:
fine open sets; \(f_\delta\)-open sets; \(f_\delta\)-closed sets; \(f_\delta\)-\(g\)-closed set; \(f_\delta\)-separation axiomsReferences:
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