Abstract: 
We study homeomorphism groups of metrizable compactifications of
$\mathbb{N}$. All of those groups can be represented as almost
zero-dimensional Polishable subgroups of the group $S_\infty$.
As a corollary, we show that all Polish groups are continuous
homomorphic images of almost zero-dimensional Polishable
subgroups of $S_\infty$. We prove a sufficient condition for
these groups to be one-dimensional and also study their
descriptive complexity. In the last section we associate with
every Polishable ideal on $\mathbb{N}$ a certain Polishable
subgroup of $S_\infty$ which shares its topological dimension
and descriptive complexity.

1. Department of Mathematics 253-37
   California Institute of Technology
   Pasadena, CA 91125, U.S.A.