Regular GδGδ-diagonal and mappings

In this paper, we prove that an example by Mysior has no regular GδGδ-diagonal, which can be used to show that open ≤2-to-one maps need not preserve regular GδGδ-diagonals or zero-set diagonals. We also discuss the diagonal of the Mrówka space. Let AA be a maximal almost disjoint family on NN, then for any countable subset BB of AA, the Mrówka space ψ(A∖B)ψ(A∖B) has no regular GδGδ-diagonal.