Geodesic
An example of strongly self-homeomorphic dendrite not pointwise self-homeomorphic
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 571-576.

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Such spaces in which a homeomorphic image of the whole space can be found in every open set are called {\it self-homeomorphic}. W.J. Charatonik and A. Dilks asked if any strongly self-homeomorphic dendrite is pointwise self-homeomorphic. We give a negative answer in Example 2.1.
Classification : 54C25, 54F15, 54F50
Keywords: continuum; dendrite; fan; triod; self-homeomorphic 
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Pyrih, Pavel. An example of strongly self-homeomorphic dendrite not pointwise self-homeomorphic. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 571-576. http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a15/