Epsilon-Nets

Definition

Consider a Metric Space $(X,\mathcal{T},d)$ and a positive Real Number $ϵ>0$. A finite subset $A_{ϵ}\subset X$ is called an $ϵ$-net of $X$ if for every point $x\in X$, there exists an element $a\in A_{ϵ}$ such that the distance between $a$ and $x$ is less than $ϵ$. $A_{ϵ}\subset X\text{s.t.}|A_{ϵ}|<\infty \text{and}\forall x\in X,\exists a\in A_{ϵ}\text{s.t.}d(x,a)<ϵ$