EXTREME POINT

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-coordinates 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 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.