Cauchy net

In mathematics, a Cauchy net generalizes the notion of Cauchy sequence to nets defined on uniform spaces.^[1]

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.^[1][2] More generally, in a Cauchy space, a net (x_α) is Cauchy if the filter generated by the net is a Cauchy filter.

References

1. Willard, Stephen (2012), General Topology, Dover Books on Mathematics, Courier Dover Publications, p. 260, ISBN 9780486131788.
2. Joshi, K. D. (1983), Introduction to General Topology, New Age International, p. 356, ISBN 9780852264447.