Finite net
= Finite net
{title2=$G_\varepsilon$}
An $\varepsilon$-net of a <metric space> is a set $G$ such that every point lies within distance $\varepsilon$ of a point of $G$. A Cartesian grid of coordinate spacing $\eta$ is a finite $\sqrt d\,\eta$-net of a bounded cube in the <Euclidean norm>. A <Lipschitz bound> transfers control on the grid to control over the whole cube.