fa.functional analysis - Compact Convex sets and Extreme Points

[Just a historical remark.] AFAIK, the fact that the set of all extreme points of a compact convex
subset of $mathbb{R}^{2}$ must be closed is due to the legendary American
mathematician G. Baley Price (1905-2006), in "On the
extreme points of convex sets", Duke Math. J. Volume
3, Number 1 (1937), 56-67 (page 62).