Definition:Convex Hull/Definition 2

Definition

Let $V$ be a vector space over $\R$.

Let $U \subseteq V$.

The convex hull of $U$ is defined and denoted:

$\ds \map {\operatorname {conv} } U = $ the intersection of all convex sets $C \subseteq V$ of $V$ such that $U \subseteq C$.

That is, it is the intersection of all convex sets containing $U$.

Also see

• Equivalence of Definitions of Convex Hull

• Results about convex hulls can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): convex hull