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.
Famous quotes containing the word net:
“Hard times accounted in large part for the fact that the exposition was a financial disappointment in its first year, but Sally Rand and her fan dancers accomplished what applied science had failed to do, and the exposition closed in 1934 with a net profit, which was donated to participating cultural institutions, excluding Sally Rand.”
—For the State of Illinois, U.S. public relief program (1935-1943)