Let $l^p$ be the space of $p$-summable sequences. von Neumann constructed a subset of $l^p$ space $S=\{X_{mn}: m,nā„1\}$ where $X_{mn}\in l^p$ are defined by $X_{mn}(m)=1, X_{mn}(n)=m$ and $X_{mn}(k)=0$ otherwise.
I am asked to show that this $S$ is closed in the strong topology. I tried to show the complement is open by trying to construct a contradiction, but no success. Could anyone help me ? Thanks in advance.