Linked from

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

• Fixed pointBroader topic: It establishes existence even when no direct method for locating the fixed point is known.

• Fixed-point theoremBroader topic: It derives existence from continuity and the geometry of a finite-dimensional domain.

• Banach fixed-point theoremCompared with: It guarantees existence by topology, without requiring a distance-shrinking map or uniqueness.

• IntuitionismBroader topic: Brouwer's mathematical work developed alongside, but is distinct from, his intuitionist philosophy.

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

• Constructive proofCompared with: Its classical existence proof illustrates how a theorem can hold without yielding a general explicit fixed-point algorithm.

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

• Inverse function theoremCompared with: It gives global existence information, unlike the inverse function theorem's local uniqueness and structure.

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

• L. E. J. BrouwerBroader topic: This is Brouwer’s best-known topological theorem and a model of his mathematical influence.

• 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.

• Kakutani fixed-point theoremCompared with: Brouwer handles single-valued continuous maps; Kakutani extends the guarantee to correspondences.

• Rouché's theoremCompared with: It is a topological existence theorem, not a complex-analytic zero-counting criterion.

• 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.

• Lefschetz fixed-point theoremCompared with: It guarantees fixed points for a specific domain without computing a Lefschetz number.

• Boolean prime ideal theoremCompared with: Its proof and strength concern topological fixed points, not prime ideals or ultrafilters.

• Borsuk–Ulam theoremCompared with: It concerns a fixed point in a ball, whereas Borsuk–Ulam concerns equal values at opposite sphere points.

• General topologyBroader topic: It is a landmark consequence of topological structure and continuity.

• 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.

• Knaster–Tarski theoremCompared with: It relies on topology and continuity instead of lattice order and monotonicity.

• Poincaré–Birkhoff theoremCompared with: Brouwer’s result uses a ball and self-mapping condition rather than annular twist and rotation.

• Ryll-Nardzewski fixed-point theoremCompared with: Brouwer is finite-dimensional and concerns one map, unlike this common fixed-point result.

• Sharkovsky's theoremCompared with: It guarantees a fixed point from domain topology, whereas Sharkovsky’s theorem forces periods from an existing orbit.