Monotone retractions and depth of continua
Charatonik, Janusz Jerzy ; Spyrou, Panayotis
Archivum Mathematicum, Tome 030 (1994), p. 131-137 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1994-01-01
Classification:  54C10,  54F15 
@article{107501,
     author = {Janusz Jerzy Charatonik and Panayotis Spyrou},
     title = {Monotone retractions and depth of continua},
     journal = {Archivum Mathematicum},
     volume = {030},
     year = {1994},
     pages = {131-137},
     zbl = {0817.54011},
     mrnumber = {1292564},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107501}
}

Charatonik, Janusz Jerzy; Spyrou, Panayotis. Monotone retractions and depth of continua. Archivum Mathematicum, Tome 030 (1994) pp. 131-137. http://gdmltest.u-ga.fr/item/107501/

Snake-like continua, Duke Math. J. 18 (1951), 653-663. (1951) | MR 0043450 | Zbl 0043.16804

A characterization of smooth Cantor bouquets, Proc. Amer. Math. Soc. 108 (1990), 529-534. (1990) | MR 0991691

Depth of dendroids, Math. Pannonica, 5/1 (1993), 113-119. | MR 1279349

The Lelek fan is unique, Houston J. Math. 15 (1989), 27-34. (1989) | MR 1002079 | Zbl 0675.54034

Tree-likeness of dendroids and $\lambda $-dendroids, Fund. Math. 68 (1970), 19-22. (1970) | MR 0261558

On classification of hereditarily decomposable continua, Moscow Univ. Math. Bull. 29 (1974), 94-99. (1974) | MR 0367944 | Zbl 0304.54035

Topology, Springer Verlag, 1984. (1984) | MR 0734483

On plane dendroids and their end points in the classical sense, Fund. Math. 49 (1961), 301-319. (1961) | MR 0133806 | Zbl 0099.17701

Continuous mappings on continua, Dissertationes Math. (Rozprawy Mat.) 157 (1979), 1-91. (1979) | MR 0522934 | Zbl 0444.54021

The depth in tranches in $\lambda $-dendroids, Proc. Amer. Math. Soc 96 (1986), 715-720. (1986) | MR 0826508

Hyperspaces of sets, M. Dekker, 1978. (1978) | MR 0500811 | Zbl 0432.54007

On decompositions of Hausdorff continua, Dissertationes Math. (Rozprawy Mat.) 170 (1980), 1-33. (1980) | MR 0575753 | Zbl 0455.54006

Finite decompositions and the depth of a continuum, Houston J. Math. 12 (1986), 587-599. (1986) | MR 0873653 | Zbl 0713.54038