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.
@article{bwmeta1.element.bwnjournal-article-fmv150i2p113bwm,
author = {Wojciech D\k ebski and J. Heath and J. Mioduszewski},
title = {Exactly two-to-one maps from continua onto arc-continua},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {113-126},
zbl = {0856.54036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv150i2p113bwm}
}
Dębski, Wojciech; Heath, J.; Mioduszewski, J. Exactly two-to-one maps from continua onto arc-continua. Fundamenta Mathematicae, Tome 149 (1996) pp. 113-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv150i2p113bwm/
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