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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.

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.


Adding a point to configurations in closed balls
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by Lei Chen, Nir Gadish and Justin Lanier PDF
Proc. Amer. Math. Soc. 148 (2020), 885-891 Request permission


We answer the question of when a new point can be added in a continuous way to configurations of $n$ distinct points in a closed ball of arbitrary dimension. We show that this is possible given an ordered configuration of $n$ points if and only if $n \neq 1$. On the other hand, when the points are not ordered and the dimension of the ball is at least 2, a point can be added continuously if and only if $n = 2$. These results generalize the Brouwer fixed-point theorem, which gives the negative answer when $n=1$. We also show that when $n=2$, there is a unique solution to both the ordered and unordered versions of the problem up to homotopy.
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Additional Information
  • Lei Chen
  • Affiliation: Department of Mathematics, California Institute of Technology, MC 253-37, Pasadena, California 91125
  • Email:
  • Nir Gadish
  • Affiliation: Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, Illinois 60637
  • MR Author ID: 1211998
  • ORCID: 0000-0003-4479-0537
  • Email:
  • Justin Lanier
  • Affiliation: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332
  • MR Author ID: 1280905
  • ORCID: 0000-0003-4483-8553
  • Email:
  • Received by editor(s): December 19, 2018
  • Received by editor(s) in revised form: May 6, 2019, and May 20, 2019
  • Published electronically: October 18, 2019
  • Additional Notes: The third author was supported by the NSF grant DGE-1650044.
  • Communicated by: David Futer
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 885-891
  • MSC (2010): Primary 55M20, 55R80; Secondary 20F36
  • DOI:
  • MathSciNet review: 4052223