Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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.


The nonstandard treatment of Hilbert’s fifth problem
HTML articles powered by AMS MathViewer

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.
  • J. L. Bell and M. Machover, A course in mathematical logic, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. MR 0472455
  • Irving Kaplansky, Lie algebras and locally compact groups, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1995. Reprint of the 1974 edition. MR 1324106
  • J. L. Kelley and Isaac Namioka, Linear topological spaces, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. MR 0166578, DOI 10.1007/978-3-662-41914-4
  • Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104
  • Rohit Parikh, A nonstandard theory of topological groups, Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) Holt, Rinehart and Winston, New York, 1969, pp. 279–284. MR 0239964
  • Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854
  • Michael Singer, One parameter subgroups and nonstandard analysis, Manuscripta Math. 18 (1976), no. 1, 1–13. MR 396840, DOI 10.1007/BF01170531
  • L. Van Der Dries, Unpublished notes, 1981. D. T. Yang, Hilbert’s fifth problem and related problems in transformation groups, Proc. Sympos. Pure Math., vol. 28, Amer. Math. Soc., Providence, R.I., 1976, pp. 142-146.
Similar Articles
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