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Article

Charatonik, J. J. ; Spyrou, P.
Monotone retractions and depth of continua. (English). Archivum Mathematicum, vol. 30 (1994), issue 2, pp. 131-137
MSC: 54C10, 54F15 | MR 1292564 | Zbl 0817.54011
Keywords:
arclike; continuum; decomposable; dendroid; depth; end; fan; mapping; monotone; retraction; unicoherent
Summary:
It is shown that for every two countable ordinals $\alpha $ and $\beta $ with $\alpha > \beta $ there exist $\lambda $-dendroids $X$ and $Y$ whose depths are $\alpha $ and $\beta $ respectively, and a monotone retraction from $X$ onto $Y$. Moreover, the continua $X$ and $Y$ can be either both arclike or both fans.
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