Abstract
We point out the sharpness of earlier results of McMillan by exhibiting a map of the n-sphere S n , n ⩾ 5 {S^n},n \geqslant 5 , onto itself having acyclic but non-cell-like polyhedra as its nondegenerate point inverses and for which the image of the set of nondegenerate point inverses is a Cantor set K. Of necessity, K is wildly embedded, and it has the unusual additional property that every self-homeomorphism of K extends to a self-homeomorphism of S n {S^n} .
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