Abstract:Such spaces in which a homeomorphic image of the whole space can be found in every open set are called {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.
Keywords: continuum, dendrite, fan, triod, self-homeomorphic
AMS Subject Classification: 54F15, 54C25, 54F50