ψ-continuous functions

Abstract

Let \( \mathcal{T}_\psi \) be a ψ-density topology for a fixed function ψ. This paper is concerned with the family of ψ-continuous functions, that means continuous functions from (ℝ, \( \mathcal{T}_\psi \)) into (ℝ, \( \mathcal{T}_\psi \)). The family of such functions forms a lattice and is not closed under addition and uniform convergence. There exist functions ψ for which even linear functions are not ψ-continuous.