## A nonshrinkable decomposition of $S^{n}$ involving a null sequence of cellular arcs

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- by R. J. Daverman and J. J. Walsh PDF
- Trans. Amer. Math. Soc.
**272**(1982), 771-784 Request permission

## 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

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## Additional Information

- © Copyright 1982 American Mathematical Society
- 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