Mesh of a simplicial complex
= Mesh of a simplicial complex
{title2=$\mu(K)$}
For a geometrically realized simplicial complex, its mesh is
$$
\mu(K)=\sup_{\sigma\in K}\operatorname{diam}|\sigma|.
$$
If $K$ has dimension $n$, barycentric subdivision satisfies
$$
\mu(K')\leq\frac{n}{n+1}\mu(K),
$$
so $\mu(K^{(r)})\to0$.