Series Convergence

Last updated Nov 1, 2022

Let $G$ be a Topological Space and an Abelian Group and let $({a}{n}){n=1}^{\infty} \subset {G}$ be a Sequence. Then we say $\sum\limits_{n=1}^{\infty} a_{n}$ converges if $(\sum\limits_{i=1}^{n} a_{i})_{n=1}^{\infty}$ converges in $G$.