(Solution) - Let Si i I be a collection of open -(2025 Original AI-Free Solution)

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Let Si, i ? I be a collection of open convex sets.

We have encountered two distinct notions of the extremity of a set:
boundary points and extreme points. Boundary points, which demark a set from its complement, are determined by the geometry of a space. Extreme points, on the other hand, are an algebraic rather than a topological concept; they are determined solely by the linear structure of the space. However, in a normed linear space, these two notions of extremity overlap. All extreme points of a convex set are found on the boundary.