Cauchy net


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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 ba and ca, then xb-xc is in this nieghborhood.
References in periodicals archive ?
Moreover, E is an advertibly complete algebra, whenever every advertibly null Cauchy net [([x.
In particular, the consideration instead of Cauchy nets yields the class of Cauchy topologically Q-algebras, quite close indeed to Q-algebras, in effect, more close than the tQ ones.
t] becomes equality for topologically quasi-invertible elements determined by Cauchy nets, led us to consider Cauchy topologically quasi-invertible elements.