extreme point


Let C be a convex subset of a vector space X. A point xC is called an extreme pointPlanetmathPlanetmath if it is not an interior point of any line segmentMathworldPlanetmath in C. That is x is extreme if and only if whenever x=ty+(1-t)z, t(0,1), zy, implies either yC or zC.

For example the set [0,1] is a convex set and 0 and 1 are the extreme points.


  • 1 H. L. Royden. . Prentice-Hall, Englewood Cliffs, New Jersey, 1988
Title extreme point
Canonical name ExtremePoint
Date of creation 2013-03-22 14:24:55
Last modified on 2013-03-22 14:24:55
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 7
Author jirka (4157)
Entry type Definition
Classification msc 52A99
Related topic FaceOfAConvexSet
Related topic ExposedPointsAreDenseInTheExtremePoints