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 ${S^n}$.References
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Bibliographic Information
- © Copyright 1979 American Mathematical Society
- 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