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Homesimplicial approximation

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# simplicial approximation

Let $K$ and $L$ be simplicial complexes and $f:|K|\to|L|$ be a continuous function.
A simplicial mapping $g:|K|\to|L|$ which is homotopic to $f$ is called
a *simplicial approximation* of $f$.

For example, suppose that $L$ is the closure of an $n$-simplex and $a_{0}$ is a vertex of $L$. Let $f$ be a continuous map of $|K|$ to $|L|$ where $K$ is some simplicial complex. Then the map $g$ that sends all of $K$ to $a_{0}$ is a simplicial approximation of $f$.

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Reference

## Mathematics Subject Classification

55U10*no label found*

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