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On Countable Dense and n-homogeneity
Published online by Cambridge University Press: 20 November 2018
Abstract.
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 in the negative Problem 136 ofWatson in the Open Problems in Topology Book.
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- Copyright © Canadian Mathematical Society 2013
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