Spacesof continuous functions defined on Mrowka spaces

Abstract

We prove that for a maximal almost disjoint family A on omega, the space C-p(Psi (A), 2(omega)) of continuous Cantor-valued functions with the pointwise convergence topology defined on the Mrowka space Psi (A) is not normal. Using CH we construct a maximal almost disjoint family A for which the space C-p( Psi (A), 2) of continuous {0, 1}-valued functions defined on Psi (A) is Lindelof. These theorems improve some results due to Dow and Simon in [Spaces of continuous functions over a Psi-space, Preprint]. We also prove that this space C-p (Psi (A), 2) = X is a Michael space

that is, X-n is Lindelof for every n is an element of N and neither X-omega nor X x omega(omega) are normal. Moreover, we prove that for every uncountable almost disjoint family A on omega and every compactification bPsi (A) of Psi (A), the space C-p (bPsi (A), 2(omega)) is not normal. (C) 2004 Elsevier B.V. All rights reserved.