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