Combinatorial Topology

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combinatorial topology

[kəm‚bī·nə′tȯr·ē·əl tə′päl·ə·jē]
The study of polyhedrons, simplicial complexes, and generalizations of these. Also known as piecewise linear topology.

Combinatorial Topology


the branch of topology that studies topological properties of geometric figures by decomposing them into more elementary figures (a relevant example is the technique of subdividing polyhedra into simplexes) or by covering them with systems of sets. This method can be applied, as has been shown primarily by Soviet scientists, under the broadest assumptions regarding the figures being studied.


Aleksandrov, P. S. Kombinatornaia topologiia. Moscow-Leningrad, 1947.
Pontriagin, L. S. Osnovy kombinatornoi topologii. Moscow-Leningrad, 1947.
References in periodicals archive ?
With the aim of improving these enumerative results towards a more structural description, we look at the combinatorial topology of the complement M(A) := [([C.
Working from rigorous theorems and proofs, and offering a broad array of examples and applications he covers point set topology, combinatorial topology, differential topology, geometric topology and algebraic topology in chapters on continuity, compactness and connectedness, manifolds and complexes, homotopy and the winding number, fundamental group, and homology.

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