# Distance between normed spaces

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• October 16th 2010, 10:15 AM
felixgotti
Distance between normed spaces
Hi, I need to solve this problem, can someone help me?
Let c be the space of convergent scalar sequences and c0 the spaces of the null scalar sequences. Prove that the distance between them is less or equal than 3.
Thanks.
• October 16th 2010, 11:47 AM
Jose27
Quote:

Originally Posted by felixgotti
Hi, I need to solve this problem, can someone help me?
Let c be the space of convergent scalar sequences and c0 the spaces of the null scalar sequences. Prove that the distance between them is less or equal than 3.
Thanks.

What is the ambient space? What norm is this ambient space given?. Also isn't $c\cap c_0 \neq \emptyset$, so which is your definition of distance between normed spaces? (maybe this last one is the only one relevant?)