Polished A-A and added new lines for broken enumerates.

src/fa/lc/tensor.tex

@@ -23,7 +23,8 @@
         \]
 
         is a fundamental system of neighbourhoods at $0$ for $E \otimes_\pi F$.
-    \end{enumerate}
+    \end\{enumerate\}
+
     
     The space $E \otimes_\pi F$ is the \textbf{projective tensor product} of $E$ and $F$, and the mapping $\iota \in L^2(E, F; E \otimes_\pi F)$ is the \textbf{canonical embedding}.
 
@@ -72,7 +73,8 @@
     and the seminorm $\rho = p \otimes q$ is the \textbf{cross seminorm} of $p$ and $q$. Moreover, 
     \begin{enumerate}
         \item[(5)] If the seminorms $\seqi{p}$ define the topology on $E$, and the seminorms $\seqj{q}$ define the topology on $F$, then the seminorms $\bracsn{p_i \otimes q_j| (i, j) \in I \times J}$ define the topology on $E \otimes_\pi F$. 
-    \end{enumerate}
+    \end\{enumerate\}
+
     
 \end{definition}
 \begin{proof}[Proof {{\cite[III.6.3]{SchaeferWolff}}}. ]
@@ -140,7 +142,8 @@
         \item $\sum_{n \in \natp}|\lambda_n| < \infty$. 
         \item $\limv{n}x_n = 0$ and $\limv{n}y_n = 0$.
         \item $z = \sum_{n = 1}^\infty \lambda_n x_n \otimes y_n$. 
-    \end{enumerate}
+    \end\{enumerate\}
+
     
 \end{theorem}
 \begin{proof}
@@ -162,7 +165,8 @@
         \item $v_N = \sum_{k = 1}^{n_N}\lambda_{N, k}x_{N, k} \otimes y_{N, k}$.
         \item For each $1 \le k \le n_N$, $p_N(x_{N, k}), q_N(x_{N, k}) \le 1/M$.
         \item $\sum_{k = 1}^{n_N}|\lambda_k| \le 2^{-N+2}$.
-    \end{enumerate}
+    \end\{enumerate\}
+
     
     From here, let $\seqf{(x_j, y_j)} \subset X \times Y$ such that $u_1 = \sum_{j = 1}^n x_j \otimes y_j$, then
     \[