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On Countable Dense and n-homogeneity

Published online by Cambridge University Press:  20 November 2018

Jan van Mill
Jan van Mill*
Affiliation:
Mathematics, VU University Amsterdam, De Boelelaan 1081a, 1081a 1081HV, Netherlands (NL)[email protected]
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Abstract.

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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.

Keywords

54H1554C1054F05countable dense homogeneousconnectedn-homogeneousstrongly n-homogeneouscounterexample
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 4 , 01 December 2013 , pp. 860 - 869
Copyright
Copyright © Canadian Mathematical Society 2013

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