continuum; dendrite; self-homeomorphic
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 posed a problem related to strongly pointwise self-homeomorphic dendrites. We solve this problem negatively in Example 2.1.
 Charatonik, W. J., Dilks, A.: On self-homeomorphic spaces
. Topology and its Applications 55 (1994), 215 – 238. MR 1259506