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 Post subject: linear spacePosted: Mon, 21 Mar 2011 15:37:46 UTC

Joined: Sun, 6 Mar 2011 22:40:31 UTC
Posts: 7
[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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 Post subject: Re: linear spacePosted: Mon, 21 Mar 2011 15:50:44 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX
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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