Is there a word/standard terminology for when every ball $B_r$ (of finite radius $r < \infty$) in a metric space contains only finitely many points of that space?
Specifically: I am thinking about the case where $X$ is a metric space, and I have a subset $Y \subset X$ and I want to say that any ball $B_r = \{ x \in X : || x || < r\}$ contains only finitely many points of $Y$. (This is meant to generalize the analogous property for lattices such as $\mathbb Z^n \subset \mathbb R^n$.)