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The 45 pages that link to Convex set, each with the reason it gives.

• Brouwer fixed-point theoremRelated: Convexity lets the domain contract without leaving itself, a key condition in standard proofs.

• Convex functionRelated: Convex functions are defined by testing line segments within convex domains.

• Feasible regionRelated: Feasible regions defined by convex constraints are themselves convex.

• Hahn–Banach theoremRelated: Convexity underlies the theorem's geometric separation interpretation.

• Hermann MinkowskiRelated: Convex bodies are the shapes whose volume Minkowski related to lattice-point existence.

• Minimax theoremRelated: Mixed strategies form a convex set of probability distributions.

• David GaleRelated: Convexity is a recurring condition in the economic equilibrium theory Gale studied.

• Kakutani fixed-point theoremRelated: Convexity of the domain and correspondence values is a central hypothesis.

• Schauder fixed-point theoremRelated: Convexity keeps finite-dimensional approximations inside the domain.

• Hermite–Hadamard inequalityRelated: An interval is a one-dimensional convex set, the domain required by the inequality.

• Kirszbraun theoremRelated: Intersections of convex balls provide the geometric choices in extension proofs.

• Krein–Milman theoremRelated: The theorem reconstructs such a set using convex combinations of its extreme points.

• Pasch's axiomRelated: Pasch-style order reasoning helps establish how lines interact with convex regions.

• Bipolar theoremRelated: Convexity is one of the two geometric properties enforced by the bipolar.

• Brunn–Minkowski theoremRelated: Convex sets are the central geometric setting for the theorem's classical forms.

• Four-vertex theoremRelated: Convexity prevents inward indentations that would undermine the theorem’s conclusion.