Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Circle-preserving functions of spheres
HTML articles powered by AMS MathViewer

by Joel Gibbons and Cary Webb PDF
Trans. Amer. Math. Soc. 248 (1979), 67-83 Request permission

Abstract:

Suppose a function of the standard sphere ${S^2}$ into the standard sphere ${S^{2 + m}}$, $m \geqslant 0$, sends every circle into a circle but is not a circlepreserving bijection of ${S^2}$. Then the image of the function must lie in a five-point set or, if it contains more than five points, it must lie in a circle together with at most one other point. We prove the local version of this theorem together with a generalization to n dimensions. In the generalization, the significance of 5 is replaced by $2n + 1$. There is also proved a 3-dimensional result in which, compared to the n-dimensional theorem, we are allowed to weaken the structure assumed on the image set of the function.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 51M10
  • Retrieve articles in all journals with MSC: 51M10
Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 248 (1979), 67-83
  • MSC: Primary 51M10
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0521693-8
  • MathSciNet review: 521693