Inverse mapping theorem and local forms of continuous mappings (Q897972)
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scientific article; zbMATH DE number 6517538
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inverse mapping theorem and local forms of continuous mappings |
scientific article; zbMATH DE number 6517538 |
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Inverse mapping theorem and local forms of continuous mappings (English)
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8 December 2015
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The authors prove the following inverse mapping theorem (without any differentiability assumptions): Let \(f:X\to Y\) be an open discrete continuous mapping between two oriented topological manifolds of the same dimension and assume that \(|\text{deg}(f,x_0)|=1\) for some \(x_0\in X\). Then \(f\) is a local homeomorphism at \(x_0\).
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local degree
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inverse mapping theorem
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local immersion theorem
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local submersion theorem
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