A convex set $M$ is called convex body if it has nonempty interior. Interior $I(M)$ consists of elements of $M$ such that $x+ty$ is in $M$ for any $y$ and positive number $r=r(y)$ such that absolute value of $t$ smaller than $r$.
In $\ell^2$, $M$ is the set of sequences such that infinite sum of squares less than or equal to $1$. Show that $M$ is convex but not convex body.