Definition:Net (Metric Space)

Definition
Let $$M$$ be a metric space.

Let $$\epsilon > 0$$.

An $$\epsilon$$-net for $$M$$ is a subset $$S \subseteq M$$ such that:
 * $$M \subseteq \bigcup_{x \in S} N_{\epsilon} \left({x}\right)$$

where $$N_{\epsilon} \left({x}\right)$$ is the $\epsilon$-neighborhood of $$x$$.

Finite Net
A finite $$\epsilon$$-net for $$M$$ is an $$\epsilon$$-net for $$M$$ which is finite.