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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 $C$.
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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