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Search: All articles in the CJM digital archive with keyword countable dense homogeneous

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1. CJM 2013 (vol 66 pp. 759)

Hrušák, Michael; van Mill, Jan
 Addendum to "Nearly Countable Dense Homogeneous Spaces" This paper provides an addendum to M. HruÅ¡Ã¡k and J. van Mill Nearly countable dense homogeneous spaces.'' Canad. J. Math., published online 2013-03-08 http://dx.doi.org/10.4153/CJM-2013-006-8. Keywords:countable dense homogeneous, nearly countable dense homogeneous, Effros Theorem, Vaught's conjectureCategories:54H05, 03E15, 54E50

2. CJM 2013 (vol 66 pp. 743)

Hrušák, Michael; van Mill, Jan
 Nearly Countable Dense Homogeneous Spaces We study separable metric spaces with few types of countable dense sets. We present a structure theorem for locally compact spaces having precisely $n$ types of countable dense sets: such a space contains a subset $S$ of size at most $n{-}1$ such that $S$ is invariant under all homeomorphisms of $X$ and $X\setminus S$ is countable dense homogeneous. We prove that every Borel space having fewer than $\mathfrak{c}$ types of countable dense sets is Polish. The natural question of whether every Polish space has either countably many or $\mathfrak{c}$ many types of countable dense sets, is shown to be closely related to Topological Vaught's Conjecture. Keywords:countable dense homogeneous, nearly countable dense homogeneous, Effros Theorem, Vaught's conjectureCategories:54H05, 03E15, 54E50
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