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.
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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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/

[1] Bing, R. H.: Snake-like continua. Duke Math. J. 18 (1951), 653-663. | MR | Zbl

[2] Bula, W. D., Oversteegen, L. G.: A characterization of smooth Cantor bouquets. Proc. Amer. Math. Soc. 108 (1990), 529-534. | MR

[3] Charatonik, J. J., Spyrou, P.: Depth of dendroids. Math. Pannonica, 5/1 (1993), 113-119. | MR

[4] Charatonik, W. J.: The Lelek fan is unique. Houston J. Math. 15 (1989), 27-34. | MR | Zbl

[5] Cook, H.: Tree-likeness of dendroids and $\lambda $-dendroids. Fund. Math. 68 (1970), 19-22. | MR

[6] Iliadis, S. D.: On classification of hereditarily decomposable continua. Moscow Univ. Math. Bull. 29 (1974), 94-99. | MR | Zbl

[7] Jänich, K.: Topology. Springer Verlag, 1984. | MR

[8] Lelek, A.: On plane dendroids and their end points in the classical sense. Fund. Math. 49 (1961), 301-319. | MR | Zbl

[9] Mackowiak, T.: Continuous mappings on continua. Dissertationes Math. (Rozprawy Mat.) 157 (1979), 1-91. | MR | Zbl

[10] Mohler, L.: The depth in tranches in $\lambda $-dendroids. Proc. Amer. Math. Soc 96 (1986), 715-720. | MR

[11] Nadler, S. B., Jr.: Hyperspaces of sets. M. Dekker, 1978. | MR | Zbl

[12] Rakowski, Z .M.: On decompositions of Hausdorff continua. Dissertationes Math. (Rozprawy Mat.) 170 (1980), 1-33. | MR | Zbl

[13] Spyrou, P.: Finite decompositions and the depth of a continuum. Houston J. Math. 12 (1986), 587-599. | MR | Zbl