On self-homeomorphic dendrites

Janusz Jerzy Charatonik; Paweł Krupski

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 4, page 665-673
  • ISSN: 0010-2628

Abstract

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It is shown that for every numbers m 1 , m 2 ∈ { 3 , ⋯ , ω } 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.

How to cite

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Charatonik, Janusz Jerzy, and Krupski, Paweł. "On self-homeomorphic dendrites." Commentationes Mathematicae Universitatis Carolinae 43.4 (2002): 665-673. <http://eudml.org/doc/248974>.

@article{Charatonik2002,
abstract = {It is shown that for every numbers $m_1, m_2 \in \lbrace 3, \dots , \omega \rbrace $ 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.},
author = {Charatonik, Janusz Jerzy, Krupski, Paweł},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {dendrite; self-homeomorphic; dendrite; self-homeomorphism},
language = {eng},
number = {4},
pages = {665-673},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On self-homeomorphic dendrites},
url = {http://eudml.org/doc/248974},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Charatonik, Janusz Jerzy
AU - Krupski, Paweł
TI - On self-homeomorphic dendrites
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 4
SP - 665
EP - 673
AB - It is shown that for every numbers $m_1, m_2 \in \lbrace 3, \dots , \omega \rbrace $ 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.
LA - eng
KW - dendrite; self-homeomorphic; dendrite; self-homeomorphism
UR - http://eudml.org/doc/248974
ER -

References

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  1. Charatonik J.J., Charatonik W.J., Strongly chaotic dendrites, Colloq. Math. 70 (1996), 181-190. (1996) Zbl0860.54030MR1380374
  2. Charatonik J.J., Charatonik W.J., Dendrites, Aportaciones Mat. Comun. 22 (1998), 227-253. (1998) Zbl0967.54034MR1787331
  3. Charatonik W.J., Dilks A., On self-homeomorphic spaces, Topology Appl. 55 (1994), 215-238. (1994) Zbl0788.54040MR1259506
  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. (1993) Zbl0826.54027MR1235359
  5. Kuratowski K., Topology, vol. 2 Academic Press and PWN New York, London, Warszawa (1968). (1968) MR0259836
  6. Nadler S.B., Jr., Continuum Theory: An Introduction, M. Dekker (1992). (1992) Zbl0757.54009MR1192552
  7. Pyrih P., An example of strongly self-homeomorphic dendrite not pointwise self-homeomorphic, Comment. Math. Univ. Carolinae 40 (1999), 571-576. (1999) Zbl1010.54038MR1732479

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