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simplicial approximation
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(Definition)
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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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"simplicial approximation" is owned by Mathprof.
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Cross-references: map, vertex, closure, homotopic, simplicial mapping, continuous function, simplicial complexes
There are 2 references to this entry.
This is version 3 of simplicial approximation, born on 2007-04-08, modified 2007-04-08.
Object id is 9166, canonical name is SimplicialApproximation.
Accessed 1063 times total.
Classification:
| AMS MSC: | 55U10 (Algebraic topology :: Applied homological algebra and category theory :: Simplicial sets and complexes) |
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Pending Errata and Addenda
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