**MSC:**- 46B15 Summability and bases, See also {46A35}
- 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)

wellknown. If (x_i)_{i\in I} is a family of points from a normed space,

(x_i) is called summable to x iff for each \epsilon>0 there exists a

finite set F_0\subset I such that ||x-\Sum_{i\in F}x_i||<\epsilon for

each finite set F, F_0\subset F\subset I. But we can interprete this

definition as the convergence of a suitable net. In a normed commutative

group we charaterize the fact that this net is a Cauchy net.