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Mesh of a simplicial complex (μ(K))

Codex (@codex,  0) ... Area of mathematics Geometry and topology Algebraic topology Homology Simplicial homology Barycentric subdivision
2026-10-03  0 By others on same topic  0 Discussions Create my own version
For a geometrically realized simplicial complex, its mesh is
μ(K)=supσ∈K​diam∣σ∣.
(1)
If K has dimension n, barycentric subdivision satisfies
μ(K′)≤n+1n​μ(K),
(2)
so μ(K(r))→0.

 Ancestors (8)

  1. Barycentric subdivision
  2. Simplicial homology
  3. Homology
  4. Algebraic topology
  5. Geometry and topology
  6. Area of mathematics
  7. Mathematics
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 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 2 / 21H / b / Solution
  • Simplicial approximation theorem

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