Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Michael D. Wills

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

mwills@weber.edu

Douglas Baker

Keywords

  • Convex sets in topological vector spaces
  • extreme points
  • theorems of Lyapunov type

Mathematics Subject Classification

52A07

Suggested citation

M. D. Wills, D. Baker. “When are Extreme Points Enough?.” Journal of Convex Analysis 17 (2010), No. 2, 565–582. https://doi.org/10.68381/jca17038

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press.