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

Author:
Robert J. Daverman

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

MSC:
Primary 57N60; Secondary 57N10, 57N15

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

MathSciNet review:
529237

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Abstract: We point out the sharpness of earlier results of McMillan by exhibiting a map of the *n*-sphere , 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 .

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Additional Information

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

Keywords:
Cell-like,
acyclic,
upper semicontinuous,
decomposition,
disjoint disks property,
generalized manifold,
wild Cantor set,
strongly homogeneous embedding

Article copyright:
© Copyright 1979
American Mathematical Society