Whitney Preserving Maps onto Dendrites

@article{EiichiMatsuhashi2012,
abstract = { 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. },
author = {Eiichi Matsuhashi},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {hyperspace; Whitney level; Whitney map; Whitney preserving map},
language = {eng},
number = {2},
pages = {155-163},
title = {Whitney Preserving Maps onto Dendrites},
url = {http://eudml.org/doc/281342},
volume = {60},
year = {2012},
}

TY - JOUR
AU - Eiichi Matsuhashi
TI - Whitney Preserving Maps onto Dendrites
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2012
VL - 60
IS - 2
SP - 155
EP - 163
AB - 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.
LA - eng
KW - hyperspace; Whitney level; Whitney map; Whitney preserving map
UR - http://eudml.org/doc/281342
ER -