Geodesic
Monotone retractions and depth of continua
Archivum mathematicum, Tome 30 (1994) no. 2, pp. 131-137

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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.
Classification : 54C10, 54F15
Keywords: arclike; continuum; decomposable; dendroid; depth; end; fan; mapping; monotone; retraction; unicoherent 
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     author = {Charatonik, J. J. and Spyrou, P.},
     title = {Monotone retractions and depth of continua},
     journal = {Archivum mathematicum},
     pages = {131--137},
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Charatonik, J. J.; Spyrou, P. Monotone retractions and depth of continua. Archivum mathematicum, Tome 30 (1994) no. 2, pp. 131-137. http://geodesic.mathdoc.fr/item/ARM_1994__30_2_a4/