Inverse mapping theorem and local forms of continuous mappings
| Autor: | Alexandre Paiva Barreto, Luiz Hartmann, Marcio Colombo Fenille |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Inverse function theorem
010102 general mathematics Open mapping theorem (complex analysis) 01 natural sciences 010101 applied mathematics Algebra Several complex variables Closed graph theorem Danskin's theorem Mathematics::Differential Geometry Geometry and Topology 0101 mathematics Degree of a continuous mapping Bounded inverse theorem Brouwer fixed-point theorem Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Topology and its Applications. 197:10-20 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2015.10.013 |
| Popis: | We present a homological version of the Inverse Mapping Theorem for open and discrete continuous maps between oriented topological manifolds, with assumptions on the degree of the maps, but without any assumption on differentiability. We prove that this theorem is equivalent to the known homological version of the Implicit Mapping Theorem. Additionally, we study conditions for a map between oriented topological manifolds to be locally like an injection or a projection, via alternative notions of topological immersions and submersions. |
| Databáze: | OpenAIRE |
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