Convex hull: Difference between revisions

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(the set of points that lie on or above the [[witch of Agnesi]]) has the open [[upper half-plane]] as its convex hull.<ref>This example is given by {{harvtxt|Talman|1977}}, Remark 2.6.</ref>

Convex hulls can be defined more generally in certain infinite-dimensional spaces[[topological vector space]]s, but they may not preserve compactness in these spaces. Instead, the compactness of convex hulls of compact sets, in finite-dimensional Euclidean spaces, is generalized by the [[Krein–Smulian theorem]], according to which the closed convex hull of a weakly compact subset of a [[Banach space]] (a subset that is compact under the [[weak topology]]) is weakly compact.{{sfnp|Whitley|1986}}

===Extreme points===