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.
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“The history of literature—take the net result of Tiraboshi, Warton, or Schlegel,—is a sum of a very few ideas, and of very few original tales,—all the rest being variation of these.”
—Ralph Waldo Emerson (1803–1882)