Metric net
= Metric net
{title2=$\forall x\in T\ \exists u\in U:\ d(x,u)\leq\varepsilon$}
An $\varepsilon$-net of a <metric space> $(T,d)$ is a subset $U\subseteq T$ such that every $x\in T$ has $d(x,u)\leq\varepsilon$ for some $u\in U$. Its least possible finite size is the <metric covering number> with closed balls. A maximal set with pairwise distances greater than $\varepsilon$ is an $\varepsilon$-net.