What does brouwer fixed-point theorem mean?
Definitions for brouwer fixed-point theorem
brouw·er fixed-point the·o·rem
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Wikidata
Brouwer fixed-point theorem
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f with certain properties mapping a compact convex set into itself there is a point x0 such that f = x0. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form 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.
Numerology
Chaldean Numerology
The numerical value of brouwer fixed-point theorem in Chaldean Numerology is: 2
Pythagorean Numerology
The numerical value of brouwer fixed-point theorem in Pythagorean Numerology is: 2
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"brouwer fixed-point theorem." Definitions.net. STANDS4 LLC, 2024. Web. 10 May 2024. <https://www.definitions.net/definition/brouwer+fixed-point+theorem>.
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