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- Brouwer_fixed-point_theorem abstract "Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f mapping a compact convex set into itself there is a point x0 such that f(x0) = x0. The simplest forms of Brouwer's theorem are for continuous functions f from a closed interval I in the real numbers to itself or from a closed disk D to itself. A more general form than the latter is for continuous functions from a convex compact subset K of Euclidean space to itself.Among hundreds of fixed-point theorems, Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics.In its original field, this result is one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem and the Borsuk–Ulam theorem.This gives it a place among the fundamental theorems of topology. The theorem is also used for proving deep results about differential equations and is covered in most introductory courses on differential geometry.It appears in unlikely fields such as game theory. In economics, Brouwer's fixed-point theorem and its extension, the Kakutani fixed-point theorem, play a central role in the proof of existence of general equilibrium in market economies as developed in the 1950s by economics Nobel prize winners Gérard Debreu and Kenneth Arrow.The theorem was first studied in view of work on differential equations by the French mathematicians around Poincaré and Picard.Proving results such as the Poincaré–Bendixson theorem requires the use of topological methods.This work at the end of the 19th century opened into several successive versions of the theorem. The general case was first proved in 1910 by Jacques Hadamard and by Luitzen Egbertus Jan Brouwer.".
- Brouwer_fixed-point_theorem thumbnail Poincare.jpg?width=300.
- Brouwer_fixed-point_theorem wikiPageExternalLink Brouwer_Fixed_Point_Theorem.
- Brouwer_fixed-point_theorem wikiPageExternalLink BrouwerFixedPointTheorem.html.
- Brouwer_fixed-point_theorem wikiPageExternalLink brouwertheorem.
- Brouwer_fixed-point_theorem wikiPageExternalLink kmath262.htm.
- Brouwer_fixed-point_theorem wikiPageID "4101".
- Brouwer_fixed-point_theorem wikiPageRevisionID "643794624".
- Brouwer_fixed-point_theorem first "V. I.".
- Brouwer_fixed-point_theorem hasPhotoCollection Brouwer_fixed-point_theorem.
- Brouwer_fixed-point_theorem id "B/b017670".
- Brouwer_fixed-point_theorem last "Sobolev".
- Brouwer_fixed-point_theorem title "Brouwer theorem".
- Brouwer_fixed-point_theorem subject Category:Continuous_mappings.
- Brouwer_fixed-point_theorem subject Category:Fixed-point_theorems.
- Brouwer_fixed-point_theorem subject Category:Mathematical_and_quantitative_methods_(economics).
- Brouwer_fixed-point_theorem subject Category:Theorems_in_convex_geometry.
- Brouwer_fixed-point_theorem subject Category:Theorems_in_topology.
- Brouwer_fixed-point_theorem type Abstraction100002137.
- Brouwer_fixed-point_theorem type Communication100033020.
- Brouwer_fixed-point_theorem type ContinuousMappings.
- Brouwer_fixed-point_theorem type Fixed-pointTheorems.
- Brouwer_fixed-point_theorem type Function113783816.
- Brouwer_fixed-point_theorem type MathematicalRelation113783581.
- Brouwer_fixed-point_theorem type Message106598915.
- Brouwer_fixed-point_theorem type Proposition106750804.
- Brouwer_fixed-point_theorem type Relation100031921.
- Brouwer_fixed-point_theorem type Statement106722453.
- Brouwer_fixed-point_theorem type Theorem106752293.
- Brouwer_fixed-point_theorem type TheoremsInTopology.
- Brouwer_fixed-point_theorem comment "Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f mapping a compact convex set into itself there is a point x0 such that f(x0) = x0. The simplest forms of Brouwer's theorem are for continuous functions f from a closed interval I in the real numbers to itself or from a closed disk D to itself.".
- Brouwer_fixed-point_theorem label "Brouwer fixed-point theorem".
- Brouwer_fixed-point_theorem label "Brouwer-féle fixponttétel".
- Brouwer_fixed-point_theorem label "Brouwerova věta o pevném bodu".
- Brouwer_fixed-point_theorem label "Dekpuntstelling van Brouwer".
- Brouwer_fixed-point_theorem label "Fixpunktsatz von Brouwer".
- Brouwer_fixed-point_theorem label "Teorema del punt fix de Brouwer".
- Brouwer_fixed-point_theorem label "Teorema del punto fijo de Brouwer".
- Brouwer_fixed-point_theorem label "Teorema del punto fisso di Brouwer".
- Brouwer_fixed-point_theorem label "Teorema do ponto fixo de Brouwer".
- Brouwer_fixed-point_theorem label "Théorème du point fixe de Brouwer".
- Brouwer_fixed-point_theorem label "Twierdzenie Brouwera o punkcie stałym".
- Brouwer_fixed-point_theorem label "Теорема Брауэра о неподвижной точке".
- Brouwer_fixed-point_theorem sameAs Brouwerova_věta_o_pevném_bodu.
- Brouwer_fixed-point_theorem sameAs Fixpunktsatz_von_Brouwer.
- Brouwer_fixed-point_theorem sameAs Teorema_del_punto_fijo_de_Brouwer.
- Brouwer_fixed-point_theorem sameAs Théorème_du_point_fixe_de_Brouwer.
- Brouwer_fixed-point_theorem sameAs Teorema_del_punto_fisso_di_Brouwer.
- Brouwer_fixed-point_theorem sameAs Dekpuntstelling_van_Brouwer.
- Brouwer_fixed-point_theorem sameAs Twierdzenie_Brouwera_o_punkcie_stałym.
- Brouwer_fixed-point_theorem sameAs Teorema_do_ponto_fixo_de_Brouwer.
- Brouwer_fixed-point_theorem sameAs m.01bb0.
- Brouwer_fixed-point_theorem sameAs Q1144897.
- Brouwer_fixed-point_theorem sameAs Q1144897.
- Brouwer_fixed-point_theorem sameAs Brouwer_fixed-point_theorem.
- Brouwer_fixed-point_theorem wasDerivedFrom Brouwer_fixed-point_theorem?oldid=643794624.
- Brouwer_fixed-point_theorem depiction Poincare.jpg.
- Brouwer_fixed-point_theorem isPrimaryTopicOf Brouwer_fixed-point_theorem.
