Let be a dense integral subdomain of the rational numbers and let be the positive terms of .
A net is a -Cauchy approximation if
Every -Cauchy - approximation is a Cauchy net approximation is a Cauchy net indexed by. This is because is a strictly ordered type, and thus a directed type and a strictly codirected type, with defined as for and . is defined as .
In Cauchy spaces
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Cauchy sequences
A Cauchy sequence is a Cauchy net whose index type is the natural numbers .