Let $X$ be a finite subset of $\mathbb{R}^{n}$.
And $f : w \in \mathbb{R}^{X} \rightarrow f(w) \in \mathbb{R}^{X}$ such as $f(w)(x_{i}) = w^{*}(x_{i})$
Is $f$ continuous ? (We consider $\mathbb{R}^{X}$ as a normed vector space).
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Of course $w^{*} : y \in \mathbb{R^{n}} \rightarrow \sup_{x \in X} \{ \langle x,y \rangle - w(x) \}$