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Whitney Preserving Maps onto Dendrites

Matsuhashi E.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

Vol. 60, no 2

155--163

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.

Some metric properties of hyperspaces

Bogdewicz A.

Demonstratio Mathematica

2000

Vol. 33, nr 1

135-149