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 !

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- Nov 20th 2009, 11:23 PMShanksseparability
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 ! - Nov 21st 2009, 08:38 AMJose27
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!