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 $0\le x \le 1$ ?

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