Search results
Search: MSC category 54H05
( Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] )
1. CJM 2013 (vol 66 pp. 759)
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 conjecture Categories:54H05, 03E15, 54E50 
