A “hidden” characterization of polyhedral convex sets
Volume 206 / 2011
Studia Mathematica 206 (2011), 63-74
MSC: Primary 46A55, 52A07; Secondary 52B05, 52A37.
DOI: 10.4064/sm206-1-5
Abstract
We prove that a closed convex subset $C$ of a complete linear metric space $X$ is polyhedral in its closed linear hull if and only if no infinite subset $A\subset X\setminus C$ can be hidden behind $C$ in the sense that $[x,y]\cap C\not = \emptyset $ for any distinct $x,y\in A$.
