\begin{definition}[Definition:Generalized Sum/Net Convergence]
Let $\struct {G, +}$ be a commutative topological semigroup.
Let $\sequence {g_n}_{n \mathop \in \N}$ be a sequence in $G$.
The series $\ds \sum_{n \mathop = 1}^\infty g_n$ '''converges as a net''' or '''has net convergence''' {{iff}} the generalized sum $\ds \sum \set {g_n: n \in \N}$ converges.
\end{definition}