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2008-03-11 Seminar

Danuta Borowska

On decomposition of closed, convex set theorems.

We will present Klee-Minkowski-Hirsch theorem, which states that every closed, convex set $$ A $$ can be decomposed into linearity space $$ L_{A} $$, asymptotic cone $$  C_{B_A}  $$ and convex hull of extremal points of the intersection of $$ A  $$ and the orthogonal complement of the linearity space. We will also prove that the above theorem is a generalization of well-known results.