We prove the following results. (i) Let X be a continuum such that X contains a dense arc component and let D be a dendrite with a closed set of branch points. If f:X → D is a Whitney preserving map, then f is a homeomorphism. (ii) For each dendrite D' with a dense set of branch points there exist a continuum X' containing a dense arc component and a Whitney preserving map f':X' → D' such that f' is not a homeomorphism.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-2-5,
author = {Eiichi Matsuhashi},
title = {Whitney Preserving Maps onto Dendrites},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {60},
year = {2012},
pages = {155-163},
zbl = {1247.54042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-2-5}
}
Eiichi Matsuhashi. Whitney Preserving Maps onto Dendrites. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 60 (2012) pp. 155-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-2-5/