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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 $y'_n \to y$.

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