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Cauchy net

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Cauchy net

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

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

References

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