Strongly generalized neighborhood systems

In this paper we define strongly generalized neighborhood systems (in brief strongly GNS) and study their properties. It’s proved that every generalized topology μ on X gives a unique strongly GNS ψ_μ: X → exp (exp X). We prove that if a generalized topology μ is given, then μ_ψμ = μ; and if a strongly GNS ψ is given, then ψ_μψ = ψ Strongly (ψ₁, ψ₂)-continuity is defined. We prove that f: X → Y is strongly (ψ₁, ψ₂)-continuous if and only if it is (μ_ψ1, μ_ψ2)-continuous.