Exactly two-to-one maps from continua onto arc-continua
Volume 150 / 1996
Fundamenta Mathematicae 150 (1996), 113-126 DOI: 10.4064/fm-150-2-113-126
Continuing studies on 2-to-1 maps onto indecomposable continua having only arcs as proper non-degenerate subcontinua - called here arc-continua - we drop the hypothesis of tree-likeness, and we get some conditions on the arc-continuum image that force any 2-to-1 map to be a local homeomorphism. We show that any 2-to-1 map from a continuum onto a local Cantor bundle Y is either a local homeomorphism or a retraction if Y is orientable, and that it is a local homeomorphism if Y is not orientable.