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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Cell-like closed-$0$-dimensional decompositions of $R^{3}$ are $R^{4}$ factors
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by Robert D. Edwards and Richard T. Miller PDF
Trans. Amer. Math. Soc. 215 (1976), 191-203 Request permission

Abstract:

It is proved that the product of a cell-like closed-0-dimensional upper semicontinuous decomposition of ${R^3}$ with a line is ${R^4}$. This establishes at once this feature for all the various dogbone-inspired decompositions of ${R^3}$. The proof makes use of an observation of L. Rubin that the universal cover of a wedge of circles admits a 1-1 immersion into the wedge crossed with ${R^1}$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 215 (1976), 191-203
  • MSC: Primary 57A10
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0383411-3
  • MathSciNet review: 0383411