On countable dense and strong $n$-homogeneity

Volume 214 / 2011

Jan van Mill Fundamenta Mathematicae 214 (2011), 215-239 MSC: Primary 57S05; Secondary 54H15, 54F45. DOI: 10.4064/fm214-3-2


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.


  • Jan van MillDepartment of Mathematics
    Faculty of Sciences
    VU University Amsterdam
    De Boelelaan 1081$^{\rm a}$
    1081 HV Amsterdam, The Netherlands

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