Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A nonshrinkable decomposition of $S^{n}$ 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
DOI: https://doi.org/10.1090/S0002-9947-1982-0662066-7
MathSciNet review: 662066
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $C$.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57N60, 54B15

Retrieve articles in all journals with MSC: 57N60, 54B15


Additional Information

Keywords: Upper semicontinuous decomposition, cellular, shrinkable, crumpled <IMG WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img36.gif" ALT="$n$">-cube, Disjoint Disks Property, Boundary Mismatch Property, spun decomposition, eyebolt
Article copyright: © Copyright 1982 American Mathematical Society