A Hilbert space$H$ over a field $F$ of real or complex numbers and with inner product $(\mid )$ is separable if it has a countable topological base, i. e. a family of vectors ${e}_{i}$, $i\in I$ where $I$ is at most countable, and such that every vector $v\in H$ can be uniquely represented as a series $v={\sum}_{i\in I}{a}_{i}{e}_{i}$ where ${a}_{i}\in F$ and the sum converges in the norm $\parallel x\parallel =\sqrt{(x\mid x)}$.