Terminology question What do you call a set of points with the following property?

For any point and any number $\epsilon$, you can find another point in the set that is less than $\epsilon$ away from the first point.

An example would be the rationals, because for any $\epsilon$ there is some positive rational number smaller than it, and you can just add that number to your point to get the required second point.
Thanks!

Turning my comment into an answer:
Such a set is said to be dense-in-itself. The term perfect is also sometimes used, but I prefer to avoid it, since it has other meanings in general topology. One can also describe such a set by saying that it has no isolated points. All of this terminology applies to topological spaces in general, not just to metric spaces.
