$S$ = {$x ∈ l_2$ | $x = (x_n)$, $x_n = 0$ for infinitely many $n$} in $l_2$.
My Try : I think this is a Nowhere Dense Set. I first have shown that the closure of $S$ is $S$ . Then I have shown that $int(S) = \phi$.
Am I correct? If I went wrong anywhere please correct me.
Actually I got it wrong. My try was wrong. As https://math.stackexchange.com/users/81360/omnomnomnom mentioned closure of $S$ will be whole $l_2$. So this is an Everywhere dense set. As an open ball of radius $x>0$ around any sequence in $l_2$ there exists a natural number $K$ such that $\sum_{n = k}^{\infty} x_n^2 < x/2$. So we can say the sequence whose terms are zero from the $k^{th}$ term belongs to that open ball.