Triangulation (Topology)
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, topology generalizes the notion of triangulation in a natural way as follows: A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a homeomorphism h:Kto X. Triangulation is useful in determining the properties of a topological space. For example, one can compute homology and cohomology groups of a triangulated space using simplicial homology and cohomology theories instead of more complicated homology and cohomology theories. For topological ma...
High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, topology generalizes the notion of triangulation in a natural way as follows: A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a homeomorphism h:Kto X. Triangulation is useful in determining the properties of a topological space. For example, one can compute homology and cohomology groups of a triangulated space using simplicial homology and cohomology theories instead of more complicated homology and cohomology theories. For topological manifolds, there is a slightly stronger notion of triangulation: a piecewise-linear triangulation (sometimes just called a triangulation) is a triangulation with the extra property that the link of any simplex is a piecewise-linear sphere.
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