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- 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 wikiPageLength "2973".
- Simplicial_approximation_theorem wikiPageOutDegree "23".
- Simplicial_approximation_theorem wikiPageRevisionID "648548614".
- Simplicial_approximation_theorem wikiPageWikiLink Algebraic_topology.
- Simplicial_approximation_theorem wikiPageWikiLink Barycentric_subdivision.
- Simplicial_approximation_theorem wikiPageWikiLink Category:Continuous_mappings.
- Simplicial_approximation_theorem wikiPageWikiLink Category:Simplicial_sets.
- Simplicial_approximation_theorem wikiPageWikiLink Category:Theorems_in_algebraic_topology.
- Simplicial_approximation_theorem wikiPageWikiLink Combinatorial_topology.
- Simplicial_approximation_theorem wikiPageWikiLink Compact_space.
- Simplicial_approximation_theorem wikiPageWikiLink Compactness.
- Simplicial_approximation_theorem wikiPageWikiLink Continuous_function.
- Simplicial_approximation_theorem wikiPageWikiLink Continuous_mapping.
- Simplicial_approximation_theorem wikiPageWikiLink Finitary.
- Simplicial_approximation_theorem wikiPageWikiLink Homology_(mathematics).
- Simplicial_approximation_theorem wikiPageWikiLink Homology_group.
- Simplicial_approximation_theorem wikiPageWikiLink Homology_theory.
- Simplicial_approximation_theorem wikiPageWikiLink Homotopic.
- Simplicial_approximation_theorem wikiPageWikiLink Homotopy.
- Simplicial_approximation_theorem wikiPageWikiLink L.E.J._Brouwer.
- Simplicial_approximation_theorem wikiPageWikiLink L._E._J._Brouwer.
- Simplicial_approximation_theorem wikiPageWikiLink Lebesgue_covering_dimension.
- Simplicial_approximation_theorem wikiPageWikiLink Lebesgue_covering_theorem.
- Simplicial_approximation_theorem wikiPageWikiLink Mathematics.
- Simplicial_approximation_theorem wikiPageWikiLink Pathological_(mathematics).
- Simplicial_approximation_theorem wikiPageWikiLink Piecewise.
- Simplicial_approximation_theorem wikiPageWikiLink Simplex.
- Simplicial_approximation_theorem wikiPageWikiLink Simplicial_complex.
- Simplicial_approximation_theorem wikiPageWikiLink Simplicial_map.
- Simplicial_approximation_theorem wikiPageWikiLinkText "Simplicial approximation theorem".
- Simplicial_approximation_theorem wikiPageWikiLinkText "simplicial approximation theorem".
- Simplicial_approximation_theorem hasPhotoCollection Simplicial_approximation_theorem.
- Simplicial_approximation_theorem id "Simplicial_complex".
- Simplicial_approximation_theorem title "Simplicial complex".
- Simplicial_approximation_theorem wikiPageUsesTemplate Template:Springer.
- 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 hypernym Result.
- Simplicial_approximation_theorem type Function.
- Simplicial_approximation_theorem type Mapping.
- Simplicial_approximation_theorem type Theorem.
- 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 sameAs Teorema_dellapprossimazione_simpliciale.
- Simplicial_approximation_theorem sameAs m.02sf9y.
- Simplicial_approximation_theorem sameAs Q3983972.
- Simplicial_approximation_theorem sameAs Q3983972.
- Simplicial_approximation_theorem wasDerivedFrom Simplicial_approximation_theorem?oldid=648548614.
- Simplicial_approximation_theorem isPrimaryTopicOf Simplicial_approximation_theorem.