Krein-Millman theorem

The Krein-Millman theorem states that in certain mathematical spaces called convex compact sets, the entire shape can be understood by examining its extreme points—those that cannot be written as a mix of other points. In essence, these "corner" points define the structure and help reconstruct the entire set through combinations. This theorem highlights that complex convex objects are fundamentally determined by their most "extreme" features, making it a powerful tool in fields like functional analysis and optimization.