Embedding Phenomena Based upon Decomposition Theory: Wild Cantor Sets Satisfying Strong Homogeneity Properties
Robert J. Daverman · Proceedings of the American Mathematical Society · 1979
We point out the sharpness of earlier results of McMillan by exhibiting a map of the n-sphere ${S^n},n \geqslant 5$, 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 ${S^n}$.