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