On \(β-γ\)-connectedness and \( β(γ,δ)\)-continuous functions

The aim of the paper is to introduce the notion of \(β-γ\)-separated sets and study their properties in topological spaces,then we introduce the notation of \(β-γ\)-connected and \(β-γ\)-disconnectedness. Also, \(β-γ\)-disconnected spaces are defined through \(β-γ\)-separated sets and their topological properties are studied. The characterizations of \(β-γ\)-connected spaces and their behaviour under \( β(γ,δ)\)-continuous functions are analysed. The notions of \(β-γ\)-components in a space \(X\) and \(β-γ\)-locally connected spaces are also introduced.