Added measurability in separable metric spaces.

src/topology/metric/metric.tex

@@ -0,0 +1,14 @@
+\section{Metrics}
+\label{section:metric}
+
+\begin{definition}[Metric Space]
+\label{definition:metric}
+    Let $X$ be a set and $d: X \times X$, then $d$ is a \textbf{metric} if:
+    \begin{enumerate}
+        \item[(PM1)] For any $x \in X$, $d(x, x) = 0$.
+        \item[(M)] For any $x, y \in X$ with $x \ne y$, $d(x, y) > 0$.
+        \item[(PM2)] For any $x, y \in X$, $d(x, y) = d(y, x)$.
+        \item[(PM3)] For any $x, y, z \in X$, $d(x, z) \le d(x, y) + d(y, z)$.
+    \end{enumerate}
+    The pair $(X, d)$ is a \textbf{metric space}, which comes with the metric uniformity induced by $d$, and the corresponding topology.
+\end{definition}