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...

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...

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

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

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

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...

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

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

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

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...

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

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

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

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

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...

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...

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

points in the cloud into a triangulation, a simplicial approximation of the manifold is created and its simplicial homology may be calculated. Finding techniques...

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

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

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

would refer to such a construction as a simplicial complex. The boundary operator on this triangulation/simplicial complex T is defined in the usual way:...

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

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...

Fleischner's theorem can be used to provide a 2-approximation to the bottleneck traveling salesman problem in metric spaces. A proof of Fleischner's theorem was...

tangent convex sets Simplicial complex — all vertices, line segments, triangles, tetrahedra, ..., making up a mesh Lax equivalence theorem — a consistent method...