diff --git a/src/fa/tvs/complete-metric.tex b/src/fa/tvs/complete-metric.tex index 6d5e0fc..8eefa3f 100644 --- a/src/fa/tvs/complete-metric.tex +++ b/src/fa/tvs/complete-metric.tex @@ -150,3 +150,13 @@ \end{proof} + +\begin{example} + \label{example:open-mapping-counters} + + Let $E = l^1(\natp; \complex)$ and $F$ be $l^1(\natp; \complex)$ equipped with the uniform norm, then the identity $E \to F$ is continuous but not open. + + Let $E = C^1([0, 1]; \complex)$ equipped with the uniform norm, $F = C([0, 1]; \complex)$, and $D: E \to F$ be the differentiation operator, then $D$ has closed graph, but is not continuous. +\end{example} + +