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.


54F15 Continua and generalizations
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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