Geodesic
On countable dense and strong $n$-homogeneity
Jan van Mill1
1 Department of Mathematics Faculty of Sciences VU University Amsterdam De Boelelaan 1081$^{\rm a}$ 1081 HV Amsterdam, The Netherlands
Fundamenta Mathematicae, Tome 214 (2011) no. 3, pp. 215-239

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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.
DOI : 10.4064/fm214-3-2
Keywords: prove space countable dense homogeneous set size n separates strongly n homogeneous main result construction example polish space strongly n homogeneous every nbsp countable dense homogeneous

Jan van Mill 1

1 Department of Mathematics Faculty of Sciences VU University Amsterdam De Boelelaan 1081$^{\rm a}$ 1081 HV Amsterdam, The Netherlands 
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Jan van Mill. On countable dense and strong $n$-homogeneity. Fundamenta Mathematicae, Tome 214 (2011) no. 3, pp. 215-239. doi: 10.4064/fm214-3-2

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