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Journal of Convex Analysis 17 (2010), No. 2, 565--582
Copyright Heldermann Verlag 2010

When are Extreme Points Enough?

Douglas Baker

Michael D. Wills
Dept. of Mathematics, Weber State University, Ogden, UT 84408, U.S.A.

We establish sufficient conditions for when the image a linear transformation on a compact, convex set in a real linear Hausdorff space is the same of the image of the linear transformation on the extreme points of that set. We show why several of those conditions cannot be relaxed and give an application.

Keywords: Convex sets in topological vector spaces, extreme points, theorems of Lyapunov type.

MSC: 52A07

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