Definition 1.6

Definition 1.6: If $$X$$ is a metric space, the ball of radius $$\epsilon$$ around a point $$x \in X$$ is denoted $$B(x,\epsilon)$$ and defined by:

$$B(x,\epsilon) = \{y \in X : d(x,y) < \epsilon\}$$

We usually think of $$\epsilon$$ as being a small quantity and so $$B(x,\epsilon)$$ consists of the points in $$X$$ that are "close" to $$x$$.