# What does $C[0,1]$ mean?

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

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! –  La Belle Noiseuse 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