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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$k$-regular mappings of $2^{n}$-dimensional Euclidean space
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by Michael E. Chisholm PDF
Proc. Amer. Math. Soc. 74 (1979), 187-190 Request permission

Abstract:

A map $f:X \to {R^n}$ is said to be k-regular if whenever ${x_1}, \ldots ,{x_k}$ are distinct points of X, then $f({x_1}), \ldots ,f({x_k})$ are linearly independent. Using configuration spaces and homological methods, it is shown that there does not exist a k-regular map from ${R^n}$ into ${R^{n(k - \alpha (k)) + \alpha (k) - 1}}$ where $\alpha (k)$ denotes the number of ones in the dyadic expansion of k and n is a power of 2.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 74 (1979), 187-190
  • MSC: Primary 55S99; Secondary 41A50
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0521896-8
  • MathSciNet review: 521896