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The open maping theorem between banach spaces says.

Let $T:X\to Y$ be a linear,continuous and surjective map between the banach spaces $X,Y$ then $T$ is an open map.

I need examples to show that the completeness assumption are important even in the presence of completeness of the other space. Thanks!


marked as duplicate by Norbert, Stefan Hamcke, Davide Giraudo, user1551, Lord_Farin Oct 11 '13 at 21:15

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    $\begingroup$ See this mathoverflow post for the harder part. Also, this post here. $\endgroup$ – David Mitra Oct 11 '13 at 15:45