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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 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