| Title:
|
On self-homeomorphic dendrites (English) |
| Author:
|
Charatonik, Janusz J. |
| Author:
|
Krupski, Paweł |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
665-673 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that for every numbers $m_1, m_2 \in \{3, \dots, \omega\}$ there is a strongly self-homeomorphic dendrite which is not pointwise self-homeomorphic. The set of all points at which the dendrite is pointwise self-homeomorphic is characterized. A general method of constructing a large family of dendrites with the same property is presented. (English) |
| Keyword:
|
dendrite |
| Keyword:
|
self-homeomorphic |
| MSC:
|
54F15 |
| MSC:
|
54F50 |
| idZBL:
|
Zbl 1090.54030 |
| idMR:
|
MR2045788 |
| . |
| Date available:
|
2009-01-08T19:26:01Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119355 |
| . |
| Reference:
|
[1] Charatonik J.J., Charatonik W.J.: Strongly chaotic dendrites.Colloq. Math. 70 (1996), 181-190. Zbl 0860.54030, MR 1380374 |
| Reference:
|
[2] Charatonik J.J., Charatonik W.J.: Dendrites.Aportaciones Mat. Comun. 22 (1998), 227-253. Zbl 0967.54034, MR 1787331 |
| Reference:
|
[3] Charatonik W.J., Dilks A.: On self-homeomorphic spaces.Topology Appl. 55 (1994), 215-238. Zbl 0788.54040, MR 1259506 |
| Reference:
|
[4] Charatonik W.J., Dilks Dye A., Reed J.F.: Self-homeomorphic star figures.Continuum Theory and Dynamical Systems. Papers of the conference/workshop on continuum theory and dynamical systems held at Lafayette, LA (USA), Thelma West M. Dekker New York (1993), Lect. Notes Pure Appl. Math. 149 283-290. Zbl 0826.54027, MR 1235359 |
| Reference:
|
[5] Kuratowski K.: Topology.vol. 2 Academic Press and PWN New York, London, Warszawa (1968). MR 0259836 |
| Reference:
|
[6] Nadler S.B., Jr.: Continuum Theory: An Introduction.M. Dekker (1992). Zbl 0757.54009, MR 1192552 |
| Reference:
|
[7] Pyrih P.: An example of strongly self-homeomorphic dendrite not pointwise self-homeomorphic.Comment. Math. Univ. Carolinae 40 (1999), 571-576. Zbl 1010.54038, MR 1732479 |
| . |
