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November 25th, 2018, 04:22 PM  #1 
Newbie Joined: Nov 2018 From: Canada Posts: 4 Thanks: 0  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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convergence, linear, normed, operator, space, vector 
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