Editing Convex hull (section)

===Closure operator===
The convex-hull operator has the characteristic properties of a [[closure operator]]:{{sfnp|Kiselman|2002}}
*It is ''extensive'', meaning that the convex hull of every set <math>X</math> is a superset of <math>X</math>.
*It is ''[[Monotone function#Monotonicity in order theory|non-decreasing]]'', meaning that, for every two sets <math>X</math> and <math>Y</math> with <math>X\subseteq Y</math>, the convex hull of <math>X</math> is a subset of the convex hull of <math>Y</math>.
*It is ''[[idempotence|idempotent]]'', meaning that for every <math>X</math>, the convex hull of the convex hull of <math>X</math> is the same as the convex hull of <math>X</math>.
When applied to a finite set of points, this is the closure operator of an [[antimatroid]], the shelling antimatroid of the point set.
Every antimatroid can be represented in this way by convex hulls of points in a Euclidean space of high-enough dimension.{{sfnp|Kashiwabara|Nakamura|Okamoto|2005}}