Extreme point
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2006-07-10T23:22:58Z
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[[Image:Extreme points illustration.png|thumb|right|A convex set in light blue, and its extreme points in red.]]
An '''extreme point''' or an '''extremal point''' is a point that belongs to the extremity of something.
*In [[mathematics]], an '''extreme point''' of a [[convex set]] ''S'' in a real [[vector space]] is a point in S which does not lie in any open [[line segment]] joining two points of ''S''. Intuitively, an extreme point is a "corner" of ''S''.
*In mathematics, the term should not be confused with a similar notion of '''extremal point''' which is a point where some function attains its [[extremum]]. For example, points in the plane that have minimal or maximal X-[[coordinate]]s are called extremal points in X direction. Similarly extremal points may be defined for any direction, not only in a direction of a [[coordinate axis]].
*In [[graph theory]], the leaf vertices of a [[tree (graph theory)|tree]] are sometimes called '''extremal points''' or '''extremal vertices'''.
*In [[geography]], an extreme (extremal) point is a point of land that extends farther in one direction than any other part of that land, which corresponds to the mathematical notion of extremal point in a given direction. See [[Extreme points of the world]].
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[[Category:Mathematical disambiguation]]
[[Category:Physical geography]]