On countable dense and strong $n$-homogeneity
Volume 214 / 2011
Fundamenta Mathematicae 214 (2011), 215-239
MSC: Primary 57S05; Secondary 54H15, 54F45.
DOI: 10.4064/fm214-3-2
Abstract
We prove that if a space $X$ is countable dense homogeneous and no set of size $n-1$ separates it, then $X$ is strongly $n$-homogeneous. Our main result is the construction of an example of a Polish space $X$ that is strongly $n$-homogeneous for every $n$, but not countable dense homogeneous.
