Example 12.9.7.label 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.