Linked from

The 28 pages that link to Brouwer fixed-point theorem, each with the reason it gives.

• Algebraic topologyRelated: Its standard proofs use topological invariants to rule out fixed-point-free maps.

• Winding numberRelated: Planar proofs use boundary winding to obstruct a fixed-point-free map.

• HomotopyRelated: Its standard proof uses homotopy invariance of the degree.

• Minimax theoremRelated: Von Neumann’s original proof used a fixed-point theorem of this kind.

• Differential topologyRelated: Its degree-theoretic proof illustrates how smooth methods establish topological conclusions.

• Maximal elementRelated: Its classical proof uses a maximal-element argument on partial extensions.

• Schauder fixed-point theoremRelated: Schauder’s theorem extends this finite-dimensional fixed-point principle.

• Helly's theoremRelated: Both are central finite-dimensional results, but one concerns intersections and the other fixed points.

• Hairy ball theoremRelated: Its proof is closely connected to the impossibility of a zero-free tangent field on the 2-sphere.

• Invariance of domainRelated: Brouwer’s fixed-point work belongs to the same period of topological research as invariance of domain.

• Sperner's lemmaRelated: Sperner labelings yield approximate fixed points on increasingly fine triangulations.