A new approach to ψ-continuity

Let Tψ be a ψ-density topology for a fixed function ψ. For any topological space X with the topology τ we will consider the family C (X, ℝψ) of all continuous functions f from (X, τ) into (ℝ, Tψ). The main aim of this paper is to investigate when C (X, ℝψ) is a ring. This article is based on the results achieved by M. Knox [A characterization of rings of density continuous functions, Real Anal. Exchange 31 (2005), 165-177].