Embedding phenomena based upon decomposition theory: wild Cantor sets satisfying strong homogeneity properties

Daverman, Robert J.

doi:10.1090/S0002-9939-1979-0529237-7

Embedding phenomena based upon decomposition theory: wild Cantor sets satisfying strong homogeneity properties
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by Robert J. Daverman

Proc. Amer. Math. Soc. 75 (1979), 177-182

DOI: https://doi.org/10.1090/S0002-9939-1979-0529237-7

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Abstract:

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 ${S^n}$.

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