Journal of Convex Analysis 33 (2026), No. 1&2, 197--206
Copyright Heldermann Verlag 2026
Notions of Relative Interior for Compact Convex Sets
Lu Yu
Université Paris 1 Panthéon-Sorbonne, UMR 8074, Centre d'Economie de la Sorbonne, Paris, France
yulumaths@gmail.com
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.
Keywords: Convex analysis, Banach space, relative interior.
MSC: 46N10, 46A03, 46A55, 52A07.
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