A Family of Mutually Nonhomeomorphic Separable Contractible 2-Manifolds of Cardinality $2^{2^{{\aleph }_0}}$

Bruce Blackadar

We describe a family of open subsets $M_A$ of the Moore plane, one for each subset $A$ of $\mathbb{R}$. Each of these subsets is a separable contractible (Hausdorff) 2-manifold, wh…