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November 25th, 2018, 04:22 PM   #1
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Convergence in a normed vector space - Linear operator

Having X a normed vector space. If f is a linear operator from X to ℝ and is not continuous in 0 (element of X) , how can we show that there exists a sequence xn that converges to 0 for which we have f(xn) = 1 (for all n element of ℕ).
Any help would be greatly appreciated, thank you.
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