Added compact definition.

src/topology/main/compact.tex

@@ -45,6 +45,12 @@
     then $\fB$ is a filter base consisting of closed sets. By assumption, there exists $x \in \bigcap_{i \in I}U_j^c$, so $\mathbf{U}$ is not an open cover, contradiction.
 \end{proof}
 
+\begin{definition}[Relatively Compact]
+\label{definition:relatively-compact}
+    Let $X$ be a topological space and $A \subset X$, then $A$ is \textbf{relatively compact} if $\ol A$ is compact. 
+\end{definition}
+
+
 \begin{proposition}
 \label{proposition:compact-extensions}
     Let $X$ be a topological space and $E, F \subset X$ be compact, then the following sets are compact: