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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 nonstandard proof of the Eberlein-Smulian theorem
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by Stefano Baratella and Siu-Ah Ng PDF
Proc. Amer. Math. Soc. 131 (2003), 3177-3180 Request permission

Abstract:

The Eberlein-Šmulian theorem on the equivalence of weak compactness and the finite intersection property of bounded closed convex sets is given a short elementary proof by applying Abraham Robinson’s nonstandard characterization of compactness.
References
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Additional Information
  • Stefano Baratella
  • Affiliation: Dipartimento di Matematica, Università di Trento, I-38050 Povo (TN), Italy
  • Email: baratell@science.unitn.it
  • Siu-Ah Ng
  • Affiliation: School of Mathematics, Statistics and Information Technology, University of Natal, Pietermaritzburg, 3209 South Africa
  • Email: ngs@nu.ac.za
  • Received by editor(s): September 11, 2001
  • Received by editor(s) in revised form: May 13, 2002
  • Published electronically: January 28, 2003
  • Additional Notes: The authors were supported by South African NRF 2039556 and Progetto Tematico GNSAGA “Teoria dei Modelli ed Applicazioni”
  • Communicated by: N. Tomczak-Jaegermann
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 3177-3180
  • MSC (2000): Primary 46B04; Secondary 46B10, 46B08
  • DOI: https://doi.org/10.1090/S0002-9939-03-06894-1
  • MathSciNet review: 1992858