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\item[(M)] For any $x, y \in X$ with $x \ne y$, $d(x, y) > 0$.
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\item[(PM2)] For any $x, y \in X$, $d(x, y) = d(y, x)$.
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\item[(PM3)] For any $x, y, z \in X$, $d(x, z) \le d(x, y) + d(y, z)$.
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\end\{enumerate\}
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\end{enumerate}
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The pair $(X, d)$ is a \textbf{metric space}, which comes with the metric uniformity induced by $d$, and the corresponding topology.
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\end{definition}
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