# On self-homeomorphic dendrites

Janusz Jerzy Charatonik; Paweł Krupski

Commentationes Mathematicae Universitatis Carolinae (2002)

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

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topCharatonik, 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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- 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
- Kuratowski K., Topology, vol. 2 Academic Press and PWN New York, London, Warszawa (1968). (1968) MR0259836
- Nadler S.B., Jr., Continuum Theory: An Introduction, M. Dekker (1992). (1992) Zbl0757.54009MR1192552
- 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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