Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 $ ?

share|cite|improve this question
I think it's the space on continuous functions on $[0,1]$. – k.stm Jan 23 '13 at 11:40
up vote 4 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.

share|cite|improve this answer
Thank you very much. – bakabakabaka Jan 23 '13 at 11:59
@bakabakabaka you are welcome! – Un Chien Andalou Jan 23 '13 at 12:00

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

share|cite|improve this answer
Thank you a lot . – bakabakabaka Jan 23 '13 at 11:59
:):):):):):):):) – Aang Jan 23 '13 at 12:01

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.