Let $M$ be an $R$-module ($R$ commutative ring with unity). Let $M=M_0 \supseteq M_1\supseteq M_2\supseteq\cdots$ be a chain of submodules. The topology in $M$: The open sets in $M$ are arbitrary union of the sets of the form $m+M_n$. My question is with respect to this topology why the addition map on $M$ is continuous? Thank you in advance.