Simplicial approximation theorem
= Simplicial approximation theorem
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For a finite simplicial complex $K$, a simplicial complex $L$, and a continuous map $f:|K|\to|L|$, some <iterated barycentric subdivision> $K^{(r)}$ admits a <simplicial approximation> to $f$. The proof applies the <Lebesgue number lemma> to the inverse images of target open stars and uses that the <mesh of a simplicial complex> tends to zero under repeated barycentric subdivision.