Added counter examples to the open mapping theorem.

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}
+
+