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Exactly two-to-one maps from continua onto arc-continua. (English) Zbl 0856.54036
An arc-continuum is a continuum with the property that every proper nondegenerate subcontinuum is an arc. The authors prove that if $$Y$$ is an indecomposable arc-continuum, which is a local Cantor bundle, then any two-to-one map from a continuum onto $$Y$$ is either a local homeomorphism or a retraction if $$Y$$ is orientable, and it is a local homeomorphism if $$Y$$ is not orientable. In the sequel, by imposing some other rather technical conditions on the image space $$Y$$, they prove that any two-to-one map from a continuum onto $$Y$$ is a local homeomorphism.

##### MSC:
 54F15 Continua and generalizations 54C10 Special maps on topological spaces (open, closed, perfect, etc.)
##### Keywords:
local bundle; arc-continuum; local homeomorphism
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