  We study two form of selective selective separability, $SS$ and $SS^+$, on
countable spaces with an analytic topology. We show several Ramsey type
properties which imply $SS$. For analytic spaces $X$, $SS^+$ is equivalent to
have that the collection of dense sets is a $G_\delta$ subset of $2^X$, and
also equivalent to the existence of a weak base which is an $F_\sigma$-subset
of $2^X$. We study several examples of analytic spaces.
