# Math Help - separability

1. ## separability

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 !

2. For $L^2$ 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. $L^{\infty }$ is not so easy as the continous functions are not dense!