Editing Cauchy sequence (section)

===In topological vector spaces===
There is also a concept of Cauchy sequence for a [[topological vector space]] <math>X</math>: Pick a [[local base]] <math>B</math> for <math>X</math> about 0; then (<math>x_k</math>) is a Cauchy sequence if for each member <math>V\in B,</math> there is some number <math>N</math> such that whenever 
<math>n,m > N, x_n - x_m</math> is an element of <math>V.</math> If the topology of <math>X</math> is compatible with a [[translation-invariant metric]] <math>d,</math> the two definitions agree.