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In the context of real analysis, I have found this question:

For each $$f \in C[0,1] $$ there is a series of even polynomials , which converge uniformly on $[0,1]$ to f.


What is $C[0,1]$ ? Is it the space of functions which are continuous for $0\le x \le 1 $ ?

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I think it's the space on continuous functions on $[0,1]$. –  k.stm Jan 23 '13 at 11:40
    
This question is funny. –  Siméon Jan 23 '13 at 12:00

2 Answers 2

up vote 3 down vote accepted

yes it is, it is a space of all continuos functions from $[0,1]$ to $\mathbb{R}$, it has some mathematical structures under some specified operations, one is like they forms a vectors space over the field of reals.

so in your space $C[0,1]$, points are just a continous function, you can define operation on them like $f+g=f(x)+g(x)=(f+g)(x)$ and multiplication like, $f.g=f(x).g(x)=(fg)(x)$, called pointwise addition and pointwise multiplication.

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Thank you very much. –  bakabakabaka Jan 23 '13 at 11:59
    
@bakabakabaka you are welcome! –  Bunuelian Trick Jan 23 '13 at 12:00

set of continuous functions on the closed interval $[0,1]$

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Thank you a lot . –  bakabakabaka Jan 23 '13 at 11:59
    
:):):):):):):):) –  Aang Jan 23 '13 at 12:01

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