Definition:Separable Space/Linguistic Note

Linguistic Note on Separable Space

The thinking behind applying the word separable to the concept of a separable space arises from the idea of denseness in the context of the real number line.

For example, a subset $S \subseteq \R$ is dense if and only if any two distinct real numbers $a, b \in \R$ such that $a < b$ can be separated by an element of $S$ in the sense that there exists $s \in S$ such that $a < s < b$.

The term seems to have been coined by Maurice René Fréchet in $1906$.

Modern approaches sometimes call into question the usefulness of the term separable in this context, as it is not immediately intuitively obvious.

However, the name has stuck, and we now have to live with it.

Sources

• 1906: M. Fréchet: Sur quelques points du calcul fonctionnel (Rend. Circ. Mat. Palermo Vol. 22: pp. 1 – 72)

• Qiaochu Yuan (https://math.stackexchange.com/users/232/qiaochu-yuan), What is the significance of the term "separable" in the context of countability properties?, URL (version: 2020-05-21): https://math.stackexchange.com/q/3684771

• Henno Brandsma (https://math.stackexchange.com/users/4280/henno-brandsma), What is the significance of the term "separable" in the context of countability properties?, URL (version: 2020-05-21): https://math.stackexchange.com/q/3684798