| Title:
|
Monotone homogeneity of dendrites (English) |
| Author:
|
Charatonik, Janusz J. |
| Author:
|
Charatonik, Włodzimierz J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
361-370 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Sufficient as well as necessary conditions are studied for a dendrite or a dendroid to be homogeneous with respect to monotone mappings. The obtained results extend ones due to H. Kato and the first named author. A number of open problems are asked. (English) |
| Keyword:
|
confluent |
| Keyword:
|
dendrite |
| Keyword:
|
dendroid |
| Keyword:
|
homeomorphism |
| Keyword:
|
homogeneous |
| Keyword:
|
mapping |
| Keyword:
|
mo\-no\-tone |
| Keyword:
|
order of a point |
| Keyword:
|
ramification |
| Keyword:
|
standard |
| Keyword:
|
universal |
| MSC:
|
54C10 |
| MSC:
|
54F50 |
| MSC:
|
54H20 |
| idZBL:
|
Zbl 0886.54030 |
| idMR:
|
MR1455503 |
| . |
| Date available:
|
2009-01-08T18:31:30Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118934 |
| . |
| Reference:
|
[1] Charatonik J.J.: The property of Kelley and confluent mappings.Bull. Polish Acad. Sci. Math. 31 (1983), 375-380. Zbl 0544.54028, MR 0756917 |
| Reference:
|
[2] Charatonik J.J.: Generalized homogeneity of curves and a question of H. Kato.Bull. Polish Acad. Sci. Math. 36 (1988), 409-411. Zbl 0767.54030, MR 1101430 |
| Reference:
|
[3] Charatonik J.J.: Monotone mappings of universal dendrites.Topology Appl. 38 (1991), 163-187. Zbl 0726.54012, MR 1094549 |
| Reference:
|
[4] Charatonik J.J., Charatonik W.J., Prajs J.R.: Mapping hierarchy for dendrites.Dissertationes Math. (Rozprawy Mat.) 333 (1994), 1-52. Zbl 0822.54009, MR 1279238 |
| Reference:
|
[5] Charatonik J.J., Eberhart C.: On smooth dendroids.Fund. Math. 67 (1970), 297-322. Zbl 0192.60002, MR 0275372 |
| Reference:
|
[6] Charatonik W.J., Dilks A.: On self-homeomorphic spaces.Topology Appl. 55 (1994), 215-238. Zbl 0788.54040, MR 1259506 |
| Reference:
|
[7] Cook H., Ingram W.T., Kuperberg K.T., Lelek A., Minc P. (editors): Continua, with the Houston problem book.M. Dekker, 1995. MR 1326830 |
| Reference:
|
[8] Czuba S.T.: On dendroids with Kelley's property.Proc. Amer. Math. Soc. 102 (1988), 728-730. Zbl 0648.54030, MR 0929011 |
| Reference:
|
[9] Eberhart C., Fugate J.B., Gordh G.R., Jr.: Branchpoint covering theorems for confluent and weakly confluent maps.Proc. Amer. Math. Soc. 55 (1976), 409-415. Zbl 0335.54010, MR 0410703 |
| Reference:
|
[10] Goodkyoontz J.T., Jr.: Some functions on hyperspaces of hereditarily unicoherent continua.Fund. Math. 95 (1977), 1-10. MR 0436097 |
| Reference:
|
[11] Gordh G.R., Jr., Lum L.: Monotone retracts and some characterizations of dendrites.Proc. Amer. Math. Soc. 59 (1976), 156-158. Zbl 0304.54034, MR 0423317 |
| Reference:
|
[12] Kato H.: Generalized homogeneity of continua and a question of J.J. Charatonik.Houston J. Math. 13 (1987), 51-63. Zbl 0635.54017, MR 0884233 |
| Reference:
|
[13] Kato H.: On problems of H. Cook.Topology Appl. 26 (1987), 219-228. Zbl 0612.54042, MR 0904468 |
| Reference:
|
[14] Kuratowski K.: Topology, vol. II.Academic Press and PWN, 1968. MR 0259835 |
| Reference:
|
[15] Lum L.: A characterization of local connectivity in dendroids.in: Studies in Topology, Academic Press, 1975, pp.331-338. Zbl 0306.54050, MR 0358739 |
| Reference:
|
[16] Maćkowiak T.: Semi-confluent mappings and their invariants.Fund. Math. 69 (1973), 251-264. MR 0321044 |
| Reference:
|
[17] Maćkowiak T.: Continuous mappings on continua.Dissertationes Math. (Rozprawy Mat.) 158 (1979), 1-91. MR 0522934 |
| Reference:
|
[18] Mazurkiewicz S.: Sur les continus homogènes.Fund. Math. 5 (1924), 137-146. |
| Reference:
|
[19] Nikiel J.: A characterization of dendroids with uncountably many endpoints in the classical sense.Houston J. Math. 9 (1983), 421-432. MR 0719101 |
| Reference:
|
[20] Nikiel J.: On Gehman dendroids.Glasnik Mat. 20 (40) (1985), 203-214. Zbl 0684.54021, MR 0818624 |
| Reference:
|
[21] Whyburn G.T.: Analytic topology.Amer. Math. Soc., 1942. Zbl 0117.15804, MR 0007095 |
| . |
