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Let $K$ and $L$ be simplicial complexes and $f: |K| \to |L|$ be a continuous function.
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Let $K$ and $L$ be complexes and $f: |K| \to |L|$ be a continuous function.
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| A simplicial mapping $g: |K| \to |L|$ which is homotopic to $f$ is called |
A simplicial mapping $g: |K| \to |L|$ which is homotopic to $f$ is called |
| a \emph{simplicial approximation} of $f$. |
a \emph{simplicial approximation} of $f$. |
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| 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 $K$ |
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 $K$ |
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is some simplicial complex. Then the map $g$ that sends all of $K$ to $a_0$ is
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is some complex. Then the map $g$ that sends all of $K$ to $a_0$ is
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| a simplicial approximation of $f$. |
a simplicial approximation of $f$. |
