I was wondering how to prove a given space is separable or not.
take L^2 and L^\infty for example please !
Any idea or help is appreciated !
For $\displaystyle L^2$ you could use the fact that it's a Hilbert space, and that a Hilbert space is separable iff it has a countable orthonormal basis. $\displaystyle L^{\infty }$ is not so easy as the continous functions are not dense!