EDB — 0MH

[0MH] Prerequisites:[0KS]↺↻. If $(X,𝜏)$ satisfies the second axiom of countability, given $A\subseteq X$ there exists a countable subset $B\subseteq A$ such that $\bar{B}\supseteq A$. In particular, the whole space $X$ admits a dense countable subset: $X$ is said to be separable. The vice versa holds for example in metric spaces, see [0Q7]↺↻. See also [0SQ]↺↻ for an application in ${ℝ}^n$.