Open subspaces of countable dense homogeneous spaces
Volume 141 / 1992
Fundamenta Mathematicae 141 (1992), 101-108
DOI: 10.4064/fm_1992_141_2_1_101_108
Abstract
We construct a completely regular space which is connected, locally connected and countable dense homogeneous but not strongly locally homogeneous. The space has an open subset which has a unique cut-point. We use the construction of a $C^1$-diffeomorphism of the plane which takes one countable dense set to another.
