Separable Metric Space

Let $(X,d)$ be a metric space, and let $\mathcal{T}_d$ be the collection of subsets of $X$ that are open in $(X,d)$, which is a topology on $X$ by Metric Open Sets Form a Topology.

We say that $(X,d)$ is separable if there is a countable subset $D\subseteq X$ that is dense in $X$ for $\mathcal{T}_d$.