Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N60, 57N10, 57N15

Retrieve articles in all journals with MSC: 57N60, 57N10, 57N15

Additional Information

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