Abstract

We give an explicit example of a compact convex set without relative interior. Moreover, we show that a Banach space in which every nonempty compact convex subset has nonempty relative interior is finite dimensional. The relation between several close variants of the notion of relative interior is discussed. Finally, we generalize the Borwein-Lewis theorem on the existence of quasi relative interior.

Author information

Contact details are reproduced from the original publication and may be historical.

Lu Yu

Université Paris 1 Panthéon-Sorbonne, UMR 8074, Centre d'Economie de la Sorbonne, Paris, France

yulumaths@gmail.com

Keywords

  • Convex analysis
  • Banach space
  • relative interior

Mathematics Subject Classification

46N10, 46A03, 46A55, 52A07

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Suggested citation

L. Yu. “Notions of Relative Interior for Compact Convex Sets.” Journal of Convex Analysis 33 (2026), No. 1&2, 197–206. https://doi.org/10.68381/jca33013

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.