I was wondering if a closed cone $C$ in a Banach space $X$ of dimension at least two always has an exposed face, that is, a face $F$ such that $F=C\cap\ker\phi$ for some positive $\phi\in X^*\setminus\{0\}$.
Thanks a lot for your help!
2026-03-25 11:17:40.1774437460
Closed cones and exposed faces
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