Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Simplicial_approximation_theorem> ?p ?o. }
Showing items 1 to 35 of
35
with 100 items per page.
- Simplicial_approximation_theorem abstract "In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by a slight deformation) approximated by ones that are piecewise of the simplest kind. It applies to mappings between spaces that are built up from simplices — that is, finite simplicial complexes. The general continuous mapping between such spaces can be represented approximately by the type of mapping that is (affine-) linear on each simplex into another simplex, at the cost (i) of sufficient barycentric subdivision of the simplices of the domain, and (ii) replacement of the actual mapping by a homotopic one.This theorem was first proved by L.E.J. Brouwer, by use of the Lebesgue covering theorem (a result based on compactness). It served to put the homology theory of the time — the first decade of the twentieth century — on a rigorous basis, since it showed that the topological effect (on homology groups) of continuous mappings could in a given case be expressed in a finitary way. This must be seen against the background of a realisation at the time that continuity was in general compatible with the pathological, in some other areas. This initiated, one could say, the era of combinatorial topology.There is a further simplicial approximation theorem for homotopies, stating that a homotopy between continuous mappings can likewise be approximated by a combinatorial version.".
- Simplicial_approximation_theorem wikiPageID "583637".
- Simplicial_approximation_theorem wikiPageRevisionID "592459908".
- Simplicial_approximation_theorem hasPhotoCollection Simplicial_approximation_theorem.
- Simplicial_approximation_theorem id "Simplicial_complex".
- Simplicial_approximation_theorem title "Simplicial complex".
- Simplicial_approximation_theorem subject Category:Continuous_mappings.
- Simplicial_approximation_theorem subject Category:Simplicial_sets.
- Simplicial_approximation_theorem subject Category:Theorems_in_algebraic_topology.
- Simplicial_approximation_theorem type Abstraction100002137.
- Simplicial_approximation_theorem type Collection107951464.
- Simplicial_approximation_theorem type Communication100033020.
- Simplicial_approximation_theorem type ContinuousMappings.
- Simplicial_approximation_theorem type Function113783816.
- Simplicial_approximation_theorem type Group100031264.
- Simplicial_approximation_theorem type MathematicalRelation113783581.
- Simplicial_approximation_theorem type Message106598915.
- Simplicial_approximation_theorem type Proposition106750804.
- Simplicial_approximation_theorem type Relation100031921.
- Simplicial_approximation_theorem type Set107996689.
- Simplicial_approximation_theorem type SimplicialSets.
- Simplicial_approximation_theorem type Statement106722453.
- Simplicial_approximation_theorem type Theorem106752293.
- Simplicial_approximation_theorem type TheoremsInAlgebraicTopology.
- Simplicial_approximation_theorem type TheoremsInTopology.
- Simplicial_approximation_theorem comment "In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by a slight deformation) approximated by ones that are piecewise of the simplest kind. It applies to mappings between spaces that are built up from simplices — that is, finite simplicial complexes.".
- Simplicial_approximation_theorem label "Simplicial approximation theorem".
- Simplicial_approximation_theorem label "Teorema dell'approssimazione simpliciale".
- Simplicial_approximation_theorem sameAs Teorema_dell'approssimazione_simpliciale.
- Simplicial_approximation_theorem sameAs m.02sf9y.
- Simplicial_approximation_theorem sameAs Q3983972.
- Simplicial_approximation_theorem sameAs Q3983972.
- Simplicial_approximation_theorem sameAs Simplicial_approximation_theorem.
- Simplicial_approximation_theorem wasDerivedFrom Simplicial_approximation_theorem?oldid=592459908.
- Simplicial_approximation_theorem isPrimaryTopicOf Simplicial_approximation_theorem.