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.
@article{118934, author = {Janusz Jerzy Charatonik and W\l odzimierz J. Charatonik}, title = {Monotone homogeneity of dendrites}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {38}, year = {1997}, pages = {361-370}, zbl = {0886.54030}, mrnumber = {1455503}, language = {en}, url = {http://dml.mathdoc.fr/item/118934} }
Charatonik, Janusz Jerzy; Charatonik, Włodzimierz J. Monotone homogeneity of dendrites. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 361-370. http://gdmltest.u-ga.fr/item/118934/
The property of Kelley and confluent mappings, Bull. Polish Acad. Sci. Math. 31 (1983), 375-380. (1983) | MR 0756917 | Zbl 0544.54028
Generalized homogeneity of curves and a question of H. Kato, Bull. Polish Acad. Sci. Math. 36 (1988), 409-411. (1988) | MR 1101430 | Zbl 0767.54030
Monotone mappings of universal dendrites, Topology Appl. 38 (1991), 163-187. (1991) | MR 1094549 | Zbl 0726.54012
Mapping hierarchy for dendrites, Dissertationes Math. (Rozprawy Mat.) 333 (1994), 1-52. (1994) | MR 1279238 | Zbl 0822.54009
On smooth dendroids, Fund. Math. 67 (1970), 297-322. (1970) | MR 0275372 | Zbl 0192.60002
On self-homeomorphic spaces, Topology Appl. 55 (1994), 215-238. (1994) | MR 1259506 | Zbl 0788.54040
Continua, with the Houston problem book, M. Dekker, 1995. | MR 1326830
On dendroids with Kelley's property, Proc. Amer. Math. Soc. 102 (1988), 728-730. (1988) | MR 0929011 | Zbl 0648.54030
Branchpoint covering theorems for confluent and weakly confluent maps, Proc. Amer. Math. Soc. 55 (1976), 409-415. (1976) | MR 0410703 | Zbl 0335.54010
Some functions on hyperspaces of hereditarily unicoherent continua, Fund. Math. 95 (1977), 1-10. (1977) | MR 0436097
Monotone retracts and some characterizations of dendrites, Proc. Amer. Math. Soc. 59 (1976), 156-158. (1976) | MR 0423317 | Zbl 0304.54034
Generalized homogeneity of continua and a question of J.J. Charatonik, Houston J. Math. 13 (1987), 51-63. (1987) | MR 0884233 | Zbl 0635.54017
On problems of H. Cook, Topology Appl. 26 (1987), 219-228. (1987) | MR 0904468 | Zbl 0612.54042
Topology, vol. II, Academic Press and PWN, 1968. | MR 0259835
A characterization of local connectivity in dendroids, in: Studies in Topology, Academic Press, 1975, pp.331-338. | MR 0358739 | Zbl 0306.54050
Semi-confluent mappings and their invariants, Fund. Math. 69 (1973), 251-264. (1973) | MR 0321044
Continuous mappings on continua, Dissertationes Math. (Rozprawy Mat.) 158 (1979), 1-91. (1979) | MR 0522934
Sur les continus homogènes, Fund. Math. 5 (1924), 137-146. (1924)
A characterization of dendroids with uncountably many endpoints in the classical sense, Houston J. Math. 9 (1983), 421-432. (1983) | MR 0719101
On Gehman dendroids, Glasnik Mat. 20 (40) (1985), 203-214. (1985) | MR 0818624 | Zbl 0684.54021
Analytic topology, Amer. Math. Soc., 1942. | MR 0007095 | Zbl 0117.15804