Added properties of inductive limits.

src/fa/tvs/inductive.tex

@@ -68,3 +68,12 @@
 
     (5): By (5) of \ref{definition:tvs-inductive}.
 \end{proof}
+
+\begin{definition}[Strict]
+\label{definition:lc-inductive-strict}
+    Let $(\seqi{E}, \bracsn{\iota^i_j| i, j \in I, i \lesssim j})$ be an upward-directed system of TVSs over $K \in \RC$, then the system is \textbf{strict} if:
+    \begin{enumerate}
+        \item For each $i, j \in I$ with $i \lesssim j$, $\iota^i_j: E_i \to E_j$ is injective.
+        \item For each $i, j \in I$ with $i \lesssim j$, the topology of $E_i$ is induced by $\iota^i_j$.
+    \end{enumerate}
+\end{definition}