# Math Help - Orthogonal Complement 2

1. ## Orthogonal Complement 2

Dear Colleagues,

If $M\neq \phi$ is any subset of a Hilbert space $H$, show that $M^{\bot\bot}$ is the smallest closed subspace of $H$ which contains M, that is, $M^{\bot\bot}$ is contained in any closed subspace $Y\subset H$ such that $Y\supset M$.

Regards,

Raed.

2. What did you try ?

3. Give me a hint please and I will then continue.

4. Originally Posted by raed
Give me a hint please and I will then continue.
No, that's not how it works.

What have you tried? Where are you stuck? You have to make an effort.