  A space is functionally countable if every real-valued continuous function
has countable image. A stronger property recently defined by Tkachuk is
exponentially separability. We start by studying these properties in GO spaces,
where we extend results by Tkachuk and Wilson, and prove a conjecture by Dow.
We also study some subspaces of products that are functionally countable.
Finally, we give some examples of functionally countable spaces that are
separable and uncountable.
