Linked from

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

• Linear programmingNarrower topic: Intersections of linear half-spaces form convex feasible regions.

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

• Convex optimizationBroader topic: The feasible region must have this shape for the problem to be convex.

• Jensen's inequalityNarrower topic: Convex functions and their epigraphs are defined through this geometric property.

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

• Convex hullNarrower topic: The hull is the smallest set with this defining property that contains the given points.

• Interval (mathematics)Narrower topic: Intervals are exactly the convex subsets of the real line.

• PolyhedronNarrower topic: Intersections of half-spaces are convex, so every polyhedron has this property.

• Convex geometryBroader topic: This defining property is the starting point for the subject.

• Extreme pointNarrower topic: Extreme points are defined relative to a convex set and its line segments.

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

• ConvexityBroader topic: This is the basic set-theoretic definition of geometric convexity.

• 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.

• Carathéodory's theoremNarrower topic: Convex hulls and convex combinations are defined through this closure property.

• Convex combinationNarrower topic: Convex sets contain every convex combination of their points.

• Convex polygonNarrower topic: The polygon’s defining property is convexity applied to its interior.

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

• Simplex algorithmNarrower topic: Convexity explains why local improvement across edges can find a global optimum.

• Convex analysisBroader topic: Convex sets are the geometric objects whose intersections and boundaries underpin the subject.

• Convex bodyNarrower topic: Convexity is the defining condition inherited by every convex body.

• Support functionNarrower topic: For closed convex sets, the support function captures the set completely.

• Affine subspaceCompared with: Every affine subspace is convex, but convex sets need not be flat or closed under all affine combinations.

• 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.

• Minkowski's theorem (geometry of numbers)Narrower topic: Convexity is one of the geometric conditions that makes the lattice-point guarantee hold.

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

• BetweennessBroader topic: Betweenness identifies exactly which intervening points a convex set must contain.

• Gérard DebreuNarrower topic: Convexity assumptions help make equilibrium existence proofs work.

• Helly's theoremNarrower topic: Convexity is the geometric condition that makes the intersection criterion work.

• Gauss–Lucas theoremNarrower topic: The convex-hull conclusion relies on this geometric notion of containment.

• 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.

• Reuleaux triangleNarrower topic: The Reuleaux triangle is convex, a broader property that does not imply constant width.

• Ellipsoid methodNarrower topic: The method's cuts preserve a convex feasible region inside each enclosing ellipsoid.

• Tverberg's theoremNarrower topic: The theorem concerns intersections of convex sets formed from point groups.

• Cone (convex analysis)Narrower topic: A convex cone adds nonnegative scaling to this defining closure property.

• Hyperplane separation theoremNarrower topic: Convexity is the structural assumption that makes a separating hyperplane possible.

• 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.

• Erdős–Nagy theoremNarrower topic: Convexity is the defining property of the theorem’s final polygon.

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

• Shapley–Folkman lemmaNarrower topic: The lemma quantifies how sums of arbitrary sets approach the behavior of convex sets.