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continuum; dendrite; fan; triod; self-homeomorphic
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.
[1] Charatonik W.J., Dilks A.: On self-homeomorphic spaces. Topology Appl. 55 (1994), 215-238. MR 1259506 | Zbl 0788.54040
[2] Nadler S.B., Jr.: Continuum Theory: An Introduction. Monographs and Textbooks in Pure and Applied Math, vol. 158, Marcel Dekker, Inc., New York, N.Y. (1992). MR 1192552 | Zbl 0757.54009
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