 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-2/21h/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The mesh of a simplicial complex is the largest diameter of one of its realized simplices, or the supremum when

K

is not finite:

μ (K) = sup_{σ \in K} diam ∣ σ ∣.

dim K = n

, then

μ (K^{'}) \leq \frac{n}{n + 1} μ (K) .

Iterating gives

μ (K^{(r)}) \leq (\frac{n}{n + 1})^{r} μ (K) ⟶ 0.

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