Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the axiomatization of convex subsets of Banach spaces
HTML articles powered by AMS MathViewer

by Valerio Capraro and Tobias Fritz PDF
Proc. Amer. Math. Soc. 141 (2013), 2127-2135 Request permission

Abstract:

We prove that any convex-like structure in the sense of Nate Brown is affinely and isometrically isomorphic to a closed convex subset of a Banach space. This answers an open question of Brown. As an intermediate step, we identify Brown’s algebraic axioms as equivalent to certain well-known axioms of abstract convexity. We conclude with a new characterization of convex subsets of Banach spaces.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 52A01, 46L10
  • Retrieve articles in all journals with MSC (2010): 52A01, 46L10
Additional Information
  • Valerio Capraro
  • Affiliation: Institut de Mathématiques, University of Neuchâtel, Rue Emile-Argand 11, CH-2000 Neuchâtel, Switzerland
  • Email: valerio.capraro@unine.ch
  • Tobias Fritz
  • Affiliation: Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
  • Email: tobias.fritz@icfo.es
  • Received by editor(s): May 27, 2011
  • Received by editor(s) in revised form: September 26, 2011
  • Published electronically: January 2, 2013
  • Additional Notes: The first author was supported by Swiss SNF Sinergia project CRSI22-130435
    The second author was supported by the EU STREP QCS
  • Communicated by: Thomas Schlumprecht
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 2127-2135
  • MSC (2010): Primary 52A01; Secondary 46L10
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11465-6
  • MathSciNet review: 3034438