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joseif
 Post subject: linear space
PostPosted: Mon, 21 Mar 2011 15:37:46 UTC 
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[b]how can i prove that the set of all real-valued continuous functions defined on (0,1)
is linear space?
how can i prove that the set of all convergent sequences of real numbers are linear space?
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Shadow
 Post subject: Re: linear space
PostPosted: Mon, 21 Mar 2011 15:50:44 UTC 
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joseif wrote:
[b]how can i prove that the set of all real-valued continuous functions defined on (0,1)
is linear space?
how can i prove that the set of all convergent sequences of real numbers are linear space?


The second part is just limit laws, the first part is just that constants times continuous functions are still continous, as are sums.

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