We extend the extension by Ky Fan of the Krein–Milman theorem. The $\Phi $-extreme points of a $\Phi $-convex compact metrizable space are replaced by the $\Phi $-exposed points in the statement of Ky Fan theorem. Our main results are based on new variational principles which are of independent interest. Several applications will be given.
Due to computer-generated errors that were introduced in the typesetting stage, this article has been reprinted in its entirety in the Illinois Journal of Mathematics (Volume 62:1–4, 2018, pp. 1-24). The publisher apologizes for any inconvenience to readers.
"On the Krein–Milman–Ky Fan theorem for convex compact metrizable sets." Illinois J. Math. 61 (1-2) 1 - 24, Spring and Summer 2017. https://doi.org/10.1215/ijm/1520046206