Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function...

Banach fixed-point theorem Bekić's theorem Borel fixed-point theorem Bourbaki–Witt theorem Browder fixed-point theorem Brouwer fixed-point theorem Rothe's...

a fixed point, i.e. a point which is mapped to a set containing it. The Kakutani fixed point theorem is a generalization of the Brouwer fixed point theorem...

The Schauder fixed-point theorem is an extension of the Brouwer fixed-point theorem to topological vector spaces, which may be of infinite dimension. It...

theorem can be proved from the Brouwer fixed point theorem (in 2 dimensions), and the Brouwer fixed point theorem can be proved from the Hex theorem:...

guaranteeing that, if it is satisfied, fixed-point iteration will always converge to a fixed point. The Brouwer fixed-point theorem (1911) says that any continuous...

in his career, Brouwer proved a number of theorems in the emerging field of topology. The most important were his fixed point theorem, the topological...

In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X...

the Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important...

In mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem. They have applications, for...

The theorem and its proof are due to L. E. J. Brouwer, published in 1912. The proof uses tools of algebraic topology, notably the Brouwer fixed point theorem...

Kakutani fixed-point theorem in his 1950 paper to prove existence of equilibria. His 1951 paper used the simpler Brouwer fixed-point theorem for the same...

the Brouwer fixed-point theorem: that is, f {\displaystyle f} is continuous and maps the unit d-cube to itself. The Brouwer fixed-point theorem guarantees...

has the fixed-point property by the Brouwer fixed-point theorem. A retract A of a space X with the fixed-point property also has the fixed-point property...

Jordy Brouwer (b. 1988), Dutch footballer L. E. J. Brouwer (1881–1966), Dutch mathematician and philosopher Brouwer fixed-point theorem, Brouwer–Heyting–Kolmogorov...

mathematics, the Caristi fixed-point theorem (also known as the Caristi–Kirk fixed-point theorem) generalizes the Banach fixed-point theorem for maps of a complete...

by the Brouwer fixed-point theorem, every compact bounded convex set in a Euclidean space is a fixed-point space. The definition of a fixed-point space...

be proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem. Let Δ n − 1 {\displaystyle \Delta _{n-1}} be an ( n − 1 ) {\displaystyle...

combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that every Sperner coloring...

theorem was first proved by Henri Poincaré for the 2-sphere in 1885, and extended to higher even dimensions in 1912 by Luitzen Egbertus Jan Brouwer....

topology. The Brouwer fixed-point theorem is a related theorem that, in one dimension, gives a special case of the intermediate value theorem. In constructive...

VI (1928) 265–272. Park, Sehie (1999). "Ninety Years of the Brouwer Fixed Point Theorem" (PDF). Vietnam Journal of Mathematics. 27 (3): 187–222. CiteSeerX 10...

proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became...

equivalent to the Brouwer fixed-point theorem.: 545  It is sometimes called the Miranda theorem or the Bolzano–Poincaré–Miranda theorem. The picture on the...

the theorem. A toy theorem of the Brouwer fixed-point theorem is obtained by restricting the dimension to one. In this case, the Brouwer fixed-point theorem...

defined by Brouwer, who showed that the degree is homotopy invariant (invariant among homotopies), and used it to prove the Brouwer fixed point theorem. In modern...

diverges Banach fixed-point theorem Banach–Tarski paradox Basel problem Bolzano–Weierstrass theorem Brouwer fixed-point theorem Buckingham π theorem (proof in...

fulfilling Walras’s Law is equivalent to Brouwer fixed-Point theorem. Thus, the use of Brouwer's fixed-point theorem is essential for showing that the equilibrium...

Borsuk–Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. Here...

also has profound mathematical underpinnings related to the Brouwer fixed-point theorem, matroids and graph connectivity. The game was first published...