Cauchy net

In mathematics, a Cauchy net generalizes the notion of Cauchy sequence to nets defined on uniform spaces.

A net (xα) is a Cauchy net if for every entourage V there exists γ such that for all α, β ≥ γ, (xα, xβ) is a member of V. More generally, in a Cauchy space, a net (xα) is Cauchy if the filter generated by the net is a Cauchy filter.