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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-3-2,
author = {Jan van Mill},
title = {On countable dense and strong n-homogeneity},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {215-239},
zbl = {1248.54016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-3-2}
}
Jan van Mill. On countable dense and strong n-homogeneity. Fundamenta Mathematicae, Tome 215 (2011) pp. 215-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-3-2/