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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A nonshrinkable decomposition of $ S\sp{n}$ involving a null sequence of cellular arcs


Authors: R. J. Daverman and J. J. Walsh
Journal: Trans. Amer. Math. Soc. 272 (1982), 771-784
MSC: Primary 57N60; Secondary 54B15
MathSciNet review: 662066
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Abstract: This paper presents a decomposition $ G$ of $ S^n(n\ge 3)$ into points and a null sequence of cellular arcs such that $ S^n/G$ is not a manifold; furthermore, the union of the nondegenerate elements from $ G$ lies in a $ 2$-cell in $ S^n$ and the image in $ S^n/G$ of this union has 0-dimensional closure. Examples of nonshrinkable decompositions with a null sequence of cellular arcs have been constructed in the case $ n=3$ by D. S. Gillman and J. M. Martin and by R. H. Bing and M. Starbird. We construct another example in this dimension, for which all the arcs lie in the boundary of a crumpled cube $ C$, and then produce higher dimensional examples by spinning $ C$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0662066-7
PII: S 0002-9947(1982)0662066-7
Keywords: Upper semicontinuous decomposition, cellular, shrinkable, crumpled $ n$-cube, Disjoint Disks Property, Boundary Mismatch Property, spun decomposition, eyebolt
Article copyright: © Copyright 1982 American Mathematical Society