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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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The nonstandard treatment of Hilbert’s fifth problem
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by Joram Hirschfeld PDF
Trans. Amer. Math. Soc. 321 (1990), 379-400 Request permission


We give a nonstandard proof that every locally Euclidean group is a Lie group. The heart of the proof is a strong nonstandard variant of Gleason’s lemma for a class of groups that includes all locally Euclidean groups.
    M. Bate, Non standard analysis of Lie groups, Thesis for the degree of M. Phil., Chelsea College.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 321 (1990), 379-400
  • MSC: Primary 22E15; Secondary 03H05, 22D05, 46Q05
  • DOI:
  • MathSciNet review: 967314