1.Previous
3.Next

is always itself open, and (in Euclidean spaces) the convex hull of a compact set is always itself compact. However, there exist closed sets for which the convex hull is not closed. For instance, the closed set

:

(the set of points that lie on or above the witch of Agnesi) has the open upper half-plane as its convex hull.

Convex hulls can be defined more generally in infinite-dimensional topological vector spaces,

1.Previous
3.Next