Problem $3\mathrm{.}1\mathrm{.}3.$ Let AsubeR and let $L$ be the set of all limit points of $A.($a$)$ Show that $L$ is closed. Hint: Let $x$ be a limit point of $L$ and let $r>0.$ By definition, there exists a point $yx$ of $L$ such that yinB$(x,r).$ Now by definition of $L,$ any ball around $y$ contains a point $ay$ in $A.$ Pick such a small enough ball so that it fits inside of $B(x,r).($b$)$ Show that if