Uniform ψ-separability in iterated function spaces Cp,n(X )

A function space Cp(X) is uniformly psi-separable if there exists B subset of C(X) such that B is of countable pseudocharacter in the pointwise topology and B is dense in C(X) with the uniform topology. In this paper we study this property in the iterated function space Cp,n(X) for X in various special classes of compact spaces. The principal result of this paper is a characterization of when Cp,n(X) is uniformly psi-separable for a metrizable space X. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.