| Title:
|
Monotone retractions and depth of continua (English) |
| Author:
|
Charatonik, J. J. |
| Author:
|
Spyrou, P. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
30 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
131-137 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
arclike |
| Keyword:
|
continuum |
| Keyword:
|
decomposable |
| Keyword:
|
dendroid |
| Keyword:
|
depth |
| Keyword:
|
end |
| Keyword:
|
fan |
| Keyword:
|
mapping |
| Keyword:
|
monotone |
| Keyword:
|
retraction |
| Keyword:
|
unicoherent |
| MSC:
|
54C10 |
| MSC:
|
54F15 |
| idZBL:
|
Zbl 0817.54011 |
| idMR:
|
MR1292564 |
| . |
| Date available:
|
2008-06-06T21:26:02Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107501 |
| . |
| Reference:
|
[1] Bing, R. H.: Snake-like continua.Duke Math. J. 18 (1951), 653-663. Zbl 0043.16804, MR 0043450 |
| Reference:
|
[2] Bula, W. D., Oversteegen, L. G.: A characterization of smooth Cantor bouquets.Proc. Amer. Math. Soc. 108 (1990), 529-534. MR 0991691 |
| Reference:
|
[3] Charatonik, J. J., Spyrou, P.: Depth of dendroids.Math. Pannonica, 5/1 (1993), 113-119. MR 1279349 |
| Reference:
|
[4] Charatonik, W. J.: The Lelek fan is unique.Houston J. Math. 15 (1989), 27-34. Zbl 0675.54034, MR 1002079 |
| Reference:
|
[5] Cook, H.: Tree-likeness of dendroids and $\lambda $-dendroids.Fund. Math. 68 (1970), 19-22. MR 0261558 |
| Reference:
|
[6] Iliadis, S. D.: On classification of hereditarily decomposable continua.Moscow Univ. Math. Bull. 29 (1974), 94-99. Zbl 0304.54035, MR 0367944 |
| Reference:
|
[7] Jänich, K.: Topology.Springer Verlag, 1984. MR 0734483 |
| Reference:
|
[8] Lelek, A.: On plane dendroids and their end points in the classical sense.Fund. Math. 49 (1961), 301-319. Zbl 0099.17701, MR 0133806 |
| Reference:
|
[9] Mackowiak, T.: Continuous mappings on continua.Dissertationes Math. (Rozprawy Mat.) 157 (1979), 1-91. Zbl 0444.54021, MR 0522934 |
| Reference:
|
[10] Mohler, L.: The depth in tranches in $\lambda $-dendroids.Proc. Amer. Math. Soc 96 (1986), 715-720. MR 0826508 |
| Reference:
|
[11] Nadler, S. B., Jr.: Hyperspaces of sets.M. Dekker, 1978. Zbl 0432.54007, MR 0500811 |
| Reference:
|
[12] Rakowski, Z .M.: On decompositions of Hausdorff continua.Dissertationes Math. (Rozprawy Mat.) 170 (1980), 1-33. Zbl 0455.54006, MR 0575753 |
| Reference:
|
[13] Spyrou, P.: Finite decompositions and the depth of a continuum.Houston J. Math. 12 (1986), 587-599. Zbl 0713.54038, MR 0873653 |
| . |
