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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
##### Keywords:
cover; domain; local homeomorphism
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##### References:
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