extreme subset of convex set

Let K a non-empty closed convex subset (http://planetmath.org/ConvexSet) of a normed vector spacePlanetmathPlanetmath. A set AK is called an extreme subset of K if A is closed, convex and satisfies the condition : for any x,yK and tx+(1-t)yA,t(0,1) then x,yA.

For example let K=[0,1]×[0,1] then K, sides of K, included the endpoints, and {(1,1),(0,1),(1,0),(0,0)} are extreme subsets of K.

Title extreme subset of convex set
Canonical name ExtremeSubsetOfConvexSet
Date of creation 2013-03-22 15:24:43
Last modified on 2013-03-22 15:24:43
Owner georgiosl (7242)
Last modified by georgiosl (7242)
Numerical id 7
Author georgiosl (7242)
Entry type Definition
Classification msc 52A99
Related topic ConvexSet