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### A Topological Exercise

Posted: Thu Jul 14, 2016 12:57 pm
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 $$\mathbb{R}$$.