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 Post subject: A Topological Exercise
PostPosted: Thu Jul 14, 2016 12:57 pm 
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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 \( \mathbb{R} \).


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