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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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 $ {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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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0529237-7
PII: S 0002-9939(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