$M = \{(x_n) \in \ell_2 :\sum_{n=1}^\infty x_n = 0\}$
It is obvious that it is a linear set. But I don't know how to prove it is closed. I try to prove the complement is open, but it doesn't work. Can anyone help me?
$M = \{(x_n) \in \ell_2 :\sum_{n=1}^\infty x_n = 0\}$
It is obvious that it is a linear set. But I don't know how to prove it is closed. I try to prove the complement is open, but it doesn't work. Can anyone help me?