Definition:Generalized Sum/Net Convergence

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Definition

Let $\left({G, +}\right)$ be a commutative topological semigroup.


Let $\left({g_n}\right)_{n \in \N}$ be a sequence in $G$.

The series $\displaystyle \sum_{n \mathop = 1}^\infty g_n$ converges as a net or has net convergence if and only if the generalized sum $\displaystyle \sum \left\{{g_n: n \in \N}\right\}$ converges.


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