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Whitney Preserving Maps onto Dendrites

Volume 60 / 2012

Eiichi Matsuhashi Bulletin Polish Acad. Sci. Math. 60 (2012), 155-163 MSC: Primary 54F15, 54B20; Secondary 54C99. DOI: 10.4064/ba60-2-5

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 $f:X \to D$ 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.

Authors

  • Eiichi MatsuhashiDepartment of Mathematics
    Faculty of Engineering
    Shimane University
    Matsue, Shimane
    690-8504 Japan
    e-mail

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