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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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A weak countable choice principle
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by Douglas Bridges, Fred Richman and Peter Schuster PDF
Proc. Amer. Math. Soc. 128 (2000), 2749-2752 Request permission


A weak choice principle is introduced that is implied by both countable choice and the law of excluded middle. This principle suffices to prove that metric independence is the same as linear independence in an arbitrary normed space over a locally compact field, and to prove the fundamental theorem of algebra.
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Additional Information
  • Douglas Bridges
  • Affiliation: Department of Mathematics, University of Waikato, Hamilton, New Zealand
  • Address at time of publication: Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
  • Email:,
  • Fred Richman
  • Affiliation: Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431
  • Email:
  • Peter Schuster
  • Affiliation: Mathematisches Institut, Universität München, Theresienstraße 39, München 80333, Germany
  • Email:
  • Received by editor(s): January 26, 1998
  • Received by editor(s) in revised form: October 29, 1998
  • Published electronically: March 1, 2000
  • Communicated by: Carl G. Jockusch, Jr.
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 2749-2752
  • MSC (1991): Primary 03F65, 03E25
  • DOI:
  • MathSciNet review: 1664313