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.
@article{107692, author = {Pavel Pyrih}, title = {An example related to strongly pointwise self-homeomorphic dendrites}, journal = {Archivum Mathematicum}, volume = {035}, year = {1999}, pages = {151-154}, zbl = {1050.54524}, mrnumber = {1711732}, language = {en}, url = {http://dml.mathdoc.fr/item/107692} }
Pyrih, Pavel. An example related to strongly pointwise self-homeomorphic dendrites. Archivum Mathematicum, Tome 035 (1999) pp. 151-154. http://gdmltest.u-ga.fr/item/107692/
On self-homeomorphic spaces, Topology and its Applications 55 (1994), 215 – 238. (1994) | MR 1259506