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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!

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    Such a set is *dense-in-itself*, or *has no isolated points*. Such sets are also sometimes called *perfect* sets, but I prefer to avoid this terminology, as *perfect* has other meanings.2012-05-17

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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.