simplicial approximation theorem
Let $f:|K|\to |L|$ be continuous function^{}, where $|K|$ and $|L|$ are polyhedra having triangulations $K$ and $L$, respectively.
Then there is a barycentric subdivision ${K}^{(s)}$ of $K$ and a continuous function $g:|K|\to |L|$ such that $g$ is a simplicial map^{} from ${K}^{(s)}$ to $|L|$ and $g$ is homotopic^{} to $f$.
The theorem is due to J.W. Alexander.
References
- 1 J.W. Alexander , Combinatorial analysis situs, Trans. Amer. Math. Soc. 28, 301-329, (1926)
Title | simplicial approximation theorem |
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Canonical name | SimplicialApproximationTheorem |
Date of creation | 2013-03-22 16:54:29 |
Last modified on | 2013-03-22 16:54:29 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 5 |
Author | Mathprof (13753) |
Entry type | Theorem |
Classification | msc 55U10 |