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## A Topological Exercise

Real & Complex Analysis, Calculus & Multivariate Calculus, Functional Analysis,
Tsakanikas Nickos
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### A Topological Exercise

Let $\displaystyle X$ be a normed space. If $A$ is a non empty, open and convex subset of $X$ and if $f \in X^{*} \smallsetminus \{ 0 \}$, then show that $f(A)$ is an open interval in $\mathbb{R}$.