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Search: MSC category 54C10 ( Special maps on topological spaces (open, closed, perfect, etc.) )

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1. CMB 2012 (vol 56 pp. 860)

van Mill, Jan
On Countable Dense and $n$-homogeneity
We prove that a connected, countable dense homogeneous space is $n$-homogeneous for every $n$, and strongly 2-homogeneous provided it is locally connected. We also present an example of a connected and countable dense homogeneous space which is not strongly 2-homogeneous. This answers Problem 136 of Watson in the Open Problems in Topology Book in the negative.

Keywords:countable dense homogeneous, connected, $n$-homogeneous, strongly $n$-homogeneous, counterexample
Categories:54H15, 54C10, 54F05

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