Several terminologies in topology have as background an analogy. Let me illustrate these analogies with two examples.
For example, it is easy to accept the terminology 'reflective space' for Banach's space $X$ whose bidual $X^{\ast\ast}$ is an exact copy of $X$.That is, it makes sense to look at the bidual space $X^{\ast\ast}$ as an image reflected from the original space $X$ by the canonical application $J:X\to X^{\ast\ast}$. Here, $J(x): X^\ast\to \mathbb{R}$ is the aplicaticon $J(x)(f)=f(x)$.
Another example. Let an $X$ set be equipped as two topologies. We say that the topology $\tau_1$ is thinner than the $\tau_2$ topology if we have $\tau_2\subset \tau_1$. This means that the topology $\tau_1$ has more open than the $\tau_2$ topology. We know that the more open a topology has the harder it is to find convergent sequences in the topology. If we imagine topology as a "sieve" that lets only the convergent sequences pass, the thinner the topology, the fewer the sequences will converge.
In mathematics, a topological space is called separable if it contains a countable and dense subset.
QUESTION. What is the analogy behind the terminology "separable" to designate topological spaces that contain a subset that is both countable and dense?
I have done several researches to know the reason for this terminology in several books such as General topology (by Ryszard Engelking), Topology: a first course (by James R. Munkres) and General topology (by John L. Kelley) but I did not succeed.