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Search: MSC category 54H05 ( Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] )

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1. CJM Online first

Hrušák, Michael; Mill, Jan van
Addendum to ``Nearly Countable Dense Homogeneous Spaces'
This paper provides an addendum to M. Hrušák 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 conjecture
Categories:54H05, 03E15, 54E50

2. CJM Online first

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 conjecture
Categories:54H05, 03E15, 54E50

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