= Closed graph theorem for Fréchet spaces
{title2=$\Gamma(T)\text{ closed}\Longrightarrow T\text{ continuous}$}
A <linear map> $T:E\to F$ between <Fréchet spaces> is continuous if its <graph of a linear operator> is closed in $E\times F$. The closed graph is itself a <Fréchet space>. Its first-coordinate projection is a continuous linear bijection onto $E$, so the <open mapping theorem for Fréchet spaces> makes the inverse continuous. Compose that inverse with the second-coordinate projection to obtain $T$. Completeness of both original spaces is part of the theorem.
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