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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A nonstandard proof of the Eberlein-Smulian theorem


Authors: Stefano Baratella and Siu-Ah Ng
Journal: Proc. Amer. Math. Soc. 131 (2003), 3177-3180
MSC (2000): Primary 46B04; Secondary 46B10, 46B08
Published electronically: January 28, 2003
MathSciNet review: 1992858
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Abstract: The Eberlein-Smulian 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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06894-1
PII: S 0002-9939(03)06894-1
Keywords: Nonstandard analysis, Eberlein-\v Smulian theorem, weak compactness
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
Article copyright: © Copyright 2003 American Mathematical Society