ε-net (metric spaces)

In the mathematics of metric spaces, an $\varepsilon$ -net, or epsilon net relates to having a set which approximates another in the sense that any point in the second set is within a small distance of a point in the first (approximating) set.

Definition

An $ε$ -net is a set of points in a metric space such that each point of the space is within distance $ε$ of some point in the set. For example, if $ε > 1/2$ , then the integers are an $ε$ -net of the real numbers.

This should not be confused with the concept of a net, which is equivalent to a sequence in a metric space.