Spaces of continuous functions defined on Mrówka spaces

We prove that for a maximal almost disjoint family A on ω, the space Cp(Ψ(A),2ω) of continuous Cantor-valued functions with the pointwise convergence topology defined on the Mrówka space Ψ(A) is not normal. Using CH we construct a maximal almost disjoint family A for which the space Cp(Ψ(A),2) of continuous {0,1}-valued functions defined on Ψ(A) is Lindelöf. These theorems improve some results due to Dow and Simon in [Spaces of continuous functions over a Ψ-space, Preprint]. We also prove that this space Cp(Ψ(A),2)=X is a Michael space; that is, Xn is Lindelöf for every n∈N and neither Xω nor X×ωω are normal. Moreover, we prove that for every uncountable almost disjoint family A on ω and every compactification bΨ(A) of Ψ(A), the space Cp(bΨ(A),2ω) is not normal.