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Sufficient conditions for a local homeomorphism to be injective. (English) Zbl 0774.55003
Let \(U\) be an open connected subset of \(R^ n\) with compact closure \(\overline U\) and whose boundary \(\partial U\) has only finitely many components. The author formulates conditions for a map \(f:\overline U\to R^ n\) such that \(f| U\) is a local homeomorphism to be a homeomorphism onto its image. The conditions are of two types: first, they assume that each of the components of \(\partial U\) has, homologically speaking, some of the properties of a closed orientable \((n-1)\)-dimensional manifold, and second, they control the behavior of \(f|\partial U\) in a natural fashion.
MSC:
55M99 Classical topics in algebraic topology
55N07 Steenrod-Sitnikov homologies
57N99 Topological manifolds
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