In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by...

by the simplicial approximation theorem. A simplicial isomorphism is a bijective simplicial map such that both it and its inverse are simplicial. A simplicial...

algebraic topologists. The third theorem is perhaps the hardest. Brouwer also proved the simplicial approximation theorem in the foundations of algebraic...

identity map on odd-dimensional spheres. First, by applying the simplicial approximation theorem, one shows that if f {\displaystyle f} has no fixed points...

maps via the simplicial approximation theorem: Let K {\displaystyle {\mathcal {K}}} , L {\displaystyle {\mathcal {L}}} be abstract simplicial complexes above...

Simplex Simplicial complex Polytope Triangulation Barycentric subdivision Simplicial approximation theorem Abstract simplicial complex Simplicial set Simplicial...

Polytope Simplex Simplicial complex CW complex Manifold Triangulation Barycentric subdivision Sperner's lemma Simplicial approximation theorem Nerve of an...

equivalent to the determinacy theorem for Hex. The Lefschetz fixed-point theorem says that if a continuous map f from a finite simplicial complex B to itself has...

Davenport–Schmidt theorem (number theory, Diophantine approximations) Dirichlet's approximation theorem (Diophantine approximations) Dirichlet's theorem on arithmetic...

on the simplices and homotopic to the original maps (see also simplicial approximation). In general, such an assignment requires a refinement of the given...

Vrahatis, Michael N. (2020-04-15). "Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros". Topology and Its Applications...

spaces, such as decomposition into simplicial complexes. After the proof of the simplicial approximation theorem this approach provided rigour. The change...

Whitehead torsion vanishes. simplicial approximation See simplicial approximation theorem. simplicial complex See simplicial complex; the basic example...

precisely the CW approximation functor. Another important example is a category or more precisely the nerve of a category, which is a simplicial set. In fact...

{\displaystyle d+1} . The topological Radon theorem follows from the following more general theorem. For any simplicial complex K {\displaystyle K} , if the...

(2008), Simplicial Sets and van Kampen's Theorem (Discusses generalized versions of van Kampen's theorem applied to topological spaces and simplicial sets)...

hypothesis is equivalent to the statement that the Euler characteristic of the simplicial complex determined by the lattice of integers under divisibility is o...

the first proof of the general Stokes Theorem, and a lot more L. E. J. Brouwer: simplicial approximation theorem Élie Cartan, Georges de Rham: the notion...

of the associated orbispace. This follows by applying the simplicial approximation theorem to segments of an orbispace path lying in an orbispace chart:...

"Fundamental group". MathWorld. Dylan G.L. Allegretti, Simplicial Sets and van Kampen's Theorem: A discussion of the fundamental groupoid of a topological...

planar graph G is the 1-skeleton of a simplicial complex which is homeomorphic to the sphere. The circle packing theorem guarantees the existence of a circle...

higher analogues to the Seifert–Van Kampen theorem, without using singular homology or simplicial approximation. John Baez: Eckmann–Hilton principle (week...

bounded clique-width, but later approximation algorithms for clique-width removed this requirement. Courcelle's theorem may also be used with a stronger...

There are three known infinite families of simplicial arrangements, as well as many sporadic simplicial arrangements that do not fit into any known family...

dimensions, a more accurate approximation algorithm is known, for which the approximation error is a small multiple of the simplicial depth itself. The same...

In algebraic topology, simplicial homology is the sequence of homology groups of a simplicial complex. It formalizes the idea of the number of holes of...

(mathematics), Eben Matlis; Dualizing module, Popescu's theorem, Artin approximation theorem. This notion can be related to the spectrum of a linear operator;...

persistence methods, but may be roughly understood in the simplicial case using Hu Kuo Tin Theorem that establishes one-to-one correspondence between mutual-informations...

Nash in 1950 using the Kakutani fixed-point theorem, and later in 1951 using the Brouwer fixed-point theorem. For games with a small number of actions per...

Vrahatis, Michael N. (2020-04-15). "Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros". Topology and Its Applications...