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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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  • $\begingroup$ I think it's the space on continuous functions on $[0,1]$. $\endgroup$ – k.stm Jan 23 '13 at 11:40
  • $\begingroup$ A Google search yielded no results? $\endgroup$ – John Douma Sep 22 '19 at 17:04
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    $\begingroup$ Google search with math symbols in 2011 could easily yield no results. Google is better now... $\endgroup$ – GEdgar Sep 22 '19 at 17:22
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Yes it is. It is the space of all continuous functions from $[0,1]$ to $\mathbb{R}$. It has some mathematical structures under some specified operations. For example, $C[0,1]$ is a vector space over the field of reals.

In the space $C[0,1]$, points are just continuous functions. You can define operation on them like $(f+g)(x) =f(x)+g(x) = (f+g)(x)$ and multiplication like $(fg)(x)=f(x)g(x)=(fg)(x)$. These are called pointwise addition and pointwise multiplication.

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

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  • $\begingroup$ :):):):):):):):) $\endgroup$ – Aang Jan 23 '13 at 12:01

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