The boundary-Wecken classification of surfaces.
Answering a question of Smale, we prove that the space of C 1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
The cell-like approximation theorem of R. D. Edwards characterizes the n-manifolds precisely as the resolvable ENR homology n-manifolds with the disjoint disks property for 5 ≤ n < ∞. Since no proof for the n = 5 case has ever been published, we provide the missing details about the proof of the cell-like approximation theorem in dimension 5.