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