Spaces of continuous functions defined on Mrَwka spaces

We prove that for a maximal almost disjoint family A on ω, the space C p ( Ψ ( A ) , 2 ω ) 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 C p ( 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 C p ( Ψ ( A ) , 2 ) = X is a Michael space; that is, X n is Lindelöf for every n ∈ N and neither X ω nor X × ω ω are normal. Moreover, we prove that for every uncountable almost disjoint family A on ω and every compactification b Ψ ( A ) of Ψ ( A ) , the space C p ( b Ψ ( A ) , 2 ω ) is not normal.