A "hidden" characterization of polyhedral convex sets

Details A "hidden" characterization of polyhedral convex sets A "hidden" characterization of polyhedral convex sets

2011-06-11

arxiv.org/abs/1106.2227v2

Studia Math. 206 (2011), 63-74

Mathematics

Functional Analysis

9 pages

Scientific paper

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
$A\subset X\backslash C$ can be hidden behind $C$ in the sense $[x,y]\cap C\not
= \emptyset$ for any distinct points $x,y\in A$.

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