# extreme subset of convex set

Let $K$ a non-empty closed convex subset (http://planetmath.org/ConvexSet) of a normed vector space^{}. A set $A\subseteq K$ is called an *extreme subset* of $K$
if $A$ is closed, convex and satisfies the condition $:$ for any $x,y\in K$ and $tx+(1-t)y\in A,t\in (0,1)$ then $x,y\in A$.

For example let $K=[0,1]\times [0,1]$ 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 |
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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 |