ε-net (metric spaces)

For other uses, see Ε-net.

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 a generalization of the concept of sequence.

References

• Sutherland, W.A. (1975). Introduction to metric and topological spaces. Oxford University Press. p. 110. ISBN 0-19-853161-3. Zbl 0304.54002.