Cauchy net


Cauchy net

[′kō·shē ‚net] (mathematics) A net whose members are elements of a topological vector space and which satisfies the condition that for any neighborhood of the origin of the space there is an element a of the directed system that indexes the net such that if b and c are also members of this directed system and b ≥ a and c ≥ a, then xb-xc is in this nieghborhood.