A nonstandard proof of the EberleinSmulian theorem
Authors:
Stefano Baratella and SiuAh Ng
Journal:
Proc. Amer. Math. Soc. 131 (2003), 31773180
MSC (2000):
Primary 46B04; Secondary 46B10, 46B08
Published electronically:
January 28, 2003
MathSciNet review:
1992858
Fulltext PDF Free Access
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Abstract: The EberleinSmulian 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, I38050 Povo (TN), Italy
Email:
baratell@science.unitn.it
SiuAh 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/S0002993903068941
PII:
S 00029939(03)068941
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. TomczakJaegermann
Article copyright:
© Copyright 2003
American Mathematical Society
