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

Abstract

A function space $C_p\left(X\right)$ is uniformly ψ-separable if there exists $B\subset C\left(X\right)$ such that B is of countable pseudocharacter in the pointwise topology and B is dense in $C\left(X\right)$ with the uniform topology. In this paper we study this property in the iterated function space $C_{p,n}\left(X\right)$ for X in various special classes of compact spaces. The principal result of this paper is a characterization of when $C_{p,n}\left(X\right)$ is uniformly ψ-separable for a metrizable space X.