Construct a sequence of functions on [0,1] each of which is discontinuous at every point on [0,1] and which converges uniformly to a function that is continuous at every point?
Asked
Active
Viewed 82 times
0
-
1Any thoughts? Can you give a single example of such a discontinuous function? – lulu Jul 09 '17 at 20:01
1 Answers
1
$$ f_n(x)=\begin{cases} 0 & \text{if } x \text{ rational} \\ \frac{1}{n} & \text{if } x \text{ irrational} \end{cases} $$
Pawel
- 4,871