\(\delta^{*}\)-open sets and relation between some weak and strong forms of \(\delta^{*}\)-open sets in topological spaces

Abstract

The purpose of this present paper is to study some new classes of sets by using the open sets and functions in topological spaces. For this aim, the notions of \(\delta^{*}\)-open, \(\delta\)-\(\delta^{*}\)-\(\alpha\)-open, \(\delta\)-\(\delta^{*}\)-preopen, \(\delta\)-\(\delta^{*}\)-semiopen, \(\delta\)-\(\delta^{*}\)-\(b\)-open, \(\delta\)-\(\delta^{*}\)-\(\beta\)-open, \(\delta^{*}\)-\(\delta\)-\(\alpha\)-open, \(\delta^{*}\)-\(\delta\)-preopen, \(\delta^{*}\)-\(\delta\)-semiopen, \(\delta^{*}\)-\(\delta\)-\(b\)-open, \(\delta^{*}\)-\(\delta\)-\(\beta\)-open, \(\delta^{*}\)-\(\alpha\)-open, \(\delta^{*}\)-preopen, \(\delta^{*}\)-semiopen, \(\delta^{*}\)-\(b\)-open and \(\delta^{*}\)-\(\beta\)-open sets are introduced. Properties and the relationships of \(\delta^{*}\)-open sets are investigated. Finally, the relationships between these sets and the related concepts are investigated.