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Keywords:
dendrite; self-homeomorphic
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.
References:
[1] Charatonik J.J., Charatonik W.J.: Strongly chaotic dendrites. Colloq. Math. 70 (1996), 181-190. MR 1380374 | Zbl 0860.54030
[2] Charatonik J.J., Charatonik W.J.: Dendrites. Aportaciones Mat. Comun. 22 (1998), 227-253. MR 1787331 | Zbl 0967.54034
[3] Charatonik W.J., Dilks A.: On self-homeomorphic spaces. Topology Appl. 55 (1994), 215-238. MR 1259506 | Zbl 0788.54040
[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. MR 1235359 | Zbl 0826.54027
[5] Kuratowski K.: Topology. vol. 2 Academic Press and PWN New York, London, Warszawa (1968). MR 0259836
[6] Nadler S.B., Jr.: Continuum Theory: An Introduction. M. Dekker (1992). MR 1192552 | Zbl 0757.54009
[7] Pyrih P.: An example of strongly self-homeomorphic dendrite not pointwise self-homeomorphic. Comment. Math. Univ. Carolinae 40 (1999), 571-576. MR 1732479 | Zbl 1010.54038
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