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- Combinatorial_topology abstract "In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes . After the proof of the simplicial approximation theorem this approach provided rigour.The change of name reflected the move to organise topological classes such as cycles modulo boundaries explicitly into abelian groups. This point of view is often attributed to Emmy Noether, and so the change of title may reflect her influence. The transition is also attributed to the work of Heinz Hopf, who was influenced by Noether, and to Leopold Vietoris and Walther Mayer, who independently defined homology.A fairly precise date can be supplied in the internal notes of the Bourbaki group. While topology was still combinatorial in 1942, it had become algebraic by 1944.Rosenfeld (1973) proposed digital topology for a type of image processing that can be considered as a new development of combinatorial topology. The digital forms of Euler characteristic theorem and Gauss–Bonnet theorem were obtained by Chen et al. (See digital topology.) In history, a 2D grid cell topology had appeared in Alexandrov-Hopf's book Topologie I (1935).".
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- Combinatorial_topology wikiPageRevisionID "611208160".
- Combinatorial_topology wikiPageWikiLink Abelian_group.
- Combinatorial_topology wikiPageWikiLink Algebraic_topology.
- Combinatorial_topology wikiPageWikiLink American_Mathematical_Society.
- Combinatorial_topology wikiPageWikiLink Bar-Ilan_University.
- Combinatorial_topology wikiPageWikiLink Betti_number.
- Combinatorial_topology wikiPageWikiLink Bourbaki_group.
- Combinatorial_topology wikiPageWikiLink Category:Algebraic_topology.
- Combinatorial_topology wikiPageWikiLink Category:Combinatorics.
- Combinatorial_topology wikiPageWikiLink Digital_topology.
- Combinatorial_topology wikiPageWikiLink Emmy_Noether.
- Combinatorial_topology wikiPageWikiLink Euler_characteristic.
- Combinatorial_topology wikiPageWikiLink Gauss–Bonnet_theorem.
- Combinatorial_topology wikiPageWikiLink Grid_cell_topology.
- Combinatorial_topology wikiPageWikiLink Heinz_Hopf.
- Combinatorial_topology wikiPageWikiLink Image_processing.
- Combinatorial_topology wikiPageWikiLink Leopold_Vietoris.
- Combinatorial_topology wikiPageWikiLink Mathematics.
- Combinatorial_topology wikiPageWikiLink Nicolas_Bourbaki.
- Combinatorial_topology wikiPageWikiLink Oxford_University_Press.
- Combinatorial_topology wikiPageWikiLink Pavel_Alexandrov.
- Combinatorial_topology wikiPageWikiLink Simplicial_approximation_theorem.
- Combinatorial_topology wikiPageWikiLink Simplicial_complex.
- Combinatorial_topology wikiPageWikiLink Topological_combinatorics.
- Combinatorial_topology wikiPageWikiLink Topological_graph_theory.
- Combinatorial_topology wikiPageWikiLink Topological_invariant.
- Combinatorial_topology wikiPageWikiLink Topological_property.
- Combinatorial_topology wikiPageWikiLink Walther_Mayer.
- Combinatorial_topology wikiPageWikiLinkText "Combinatorial topology".
- Combinatorial_topology wikiPageWikiLinkText "combinatorial topology".
- Combinatorial_topology wikiPageWikiLinkText "combinatorially".
- Combinatorial_topology hasPhotoCollection Combinatorial_topology.
- Combinatorial_topology wikiPageUsesTemplate Template:Citation.
- Combinatorial_topology wikiPageUsesTemplate Template:Topology.
- Combinatorial_topology subject Category:Algebraic_topology.
- Combinatorial_topology subject Category:Combinatorics.
- Combinatorial_topology type Article.
- Combinatorial_topology type Article.
- Combinatorial_topology type Combinatoric.
- Combinatorial_topology type Field.
- Combinatorial_topology comment "In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes .".
- Combinatorial_topology label "Combinatorial topology".
- Combinatorial_topology sameAs طوبولوجيا_توافقية.
- Combinatorial_topology sameAs Topologie_combinatoire.
- Combinatorial_topology sameAs Կոմբինատորային_տոպոլոգիա.
- Combinatorial_topology sameAs m.01_pvl.
- Combinatorial_topology sameAs Q3532114.
- Combinatorial_topology sameAs Q3532114.
- Combinatorial_topology wasDerivedFrom Combinatorial_topology?oldid=611208160.
- Combinatorial_topology isPrimaryTopicOf Combinatorial_topology.