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An example of strongly self-homeomorphic dendrite not pointwise self-homeomorphic. (English) Zbl 1010.54038
Answering a question posed by W. J. Charatonik and A. Dilks [Topology Appl. 55, No. 3, 215-238 (1994; Zbl 0788.54040)], the author proves that there is a dendrite \(X\) such that every nonempty open subset contains a homeomorphic image of \(X\) having nonempty interior, and yet there is a point \(x\in X\) and its neighbourhood containing no homeomorphic image of \(X\) that would contain \(x\).

MSC:
54F50 Topological spaces of dimension \(\leq 1\); curves, dendrites
Citations:
Zbl 0788.54040
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