A nonshrinkable decomposition of 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 of into points and a null sequence of cellular arcs such that is not a manifold; furthermore, the union of the nondegenerate elements from lies in a -cell in and the image in of this union has 0-dimensional closure. Examples of nonshrinkable decompositions with a null sequence of cellular arcs have been constructed in the case 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 , and then produce higher dimensional examples by spinning .

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DOI:
https://doi.org/10.1090/S0002-9947-1982-0662066-7

Keywords:
Upper semicontinuous decomposition,
cellular,
shrinkable,
crumpled -cube,
Disjoint Disks Property,
Boundary Mismatch Property,
spun decomposition,
eyebolt

Article copyright:
© Copyright 1982
American Mathematical Society