If we know that a sequence $f_n$ of real-valued functions converges uniformly on the interval $[0,\epsilon]$ for every $\epsilon$ $\in (0,1)$, can we say that the sequence converges uniformly on the half-open interval $[0,1)$? If so, how to prove this fact rigorously? If not, what counter-exmple(s) can we give?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top