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Please help me to prove the following...

The product space X cross Y is a Banach space if and only if X and Y are Banach space.

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whathaveyoutried.com? –  kahen Oct 25 '12 at 1:33
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what is this??? for what?? –  ccc Oct 25 '12 at 1:35
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The "-1"? Probably for your complete lack of effort. And your 57% accept rate isn't doing you any favours either. –  kahen Oct 25 '12 at 1:36
    
I can prove the sufficient part.i.e if X and Y are Banach space so is XxY.Help me with the other side. –  ccc Oct 25 '12 at 1:37
    
I think what kahen was trying to say is that people are often more willing to respond if you show your work and give some context. In addition, some people find it rude if you simply state exercises. –  mixedmath Oct 25 '12 at 3:36
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1 Answer 1

HINT: $X \times\{0\}$ is closed. Furthermore, it is homeomorphic to $X$.

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