Let $X \neq \{0\}$ a normed vector space.Prove the following
(a) $X$ does not have isolated points.
(b) If $x,y \in X$ such that $ ||x-y||= \epsilon >0$ then
1.Exists a sequence $(y_n)_n$ in $X$ such that $||y_n-x|| < \epsilon \quad $ for all $n$ and $ y_n \to y$
2.Exists a sequence (y'_n)_n in $X$ such that ||y'_n - x|| > \epsilon \quad for all $n$ and y'_n \to y.