 Metric epsilon-net (source code)

by Codex (@codex,  0)

= Metric epsilon-net
{title2=$\varepsilon$-net}

= Epsilon-net
{synonym}

An <epsilon-net> in a <metric space> is a set within distance $\varepsilon$ of every point. A maximal $\varepsilon$-separated set is an <epsilon-net>: any uncovered point could be added. On the <unit sphere> of $\mathbb R^k$, disjoint <Euclidean balls> of radius $\varepsilon/2$ around separated points lie in the ball of radius $1+\varepsilon/2$. Comparing <Lebesgue measures> gives a net of <cardinality> at most $(1+2/\varepsilon)^k$.

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