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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-03-06894-1

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