Cauchy net

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

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

单词	Cauchy net
释义	Cauchy net 英语百科 Cauchy net In mathematics, a Cauchy net generalizes the notion of Cauchy sequence to nets defined on uniform spaces. A net (x_α) is a Cauchy net if for every entourage V there exists γ such that for all α, β ≥ γ, (x_α, x_β) is a member of V. More generally, in a Cauchy space, a net (x_α) is Cauchy if the filter generated by the net is a Cauchy filter.
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