Whitney Preserving Maps onto Dendrites
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 $f:X \to D$ 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 $f':X' \to D'$ such that $f'$ is not a homeomorphism.