Ψ-continuous functions and functions preserving ψ-density points

Let Tψ be the ψ-density topology for a fixed function ψ. We will examine some new properties of the family of ψ-continuous functions (that means continuous functions ƒ: ℝ →ℝ with ψ-density topology Tψ in its domain and range). In the second part of the article we will discuss functions preserving ψ-density points