Exhibit a sequence of functions that is not equicontinuous.
Solution
The family \(f_k(x) = x^k\) is not equicontinuous, since fixing \(x_0 \in (0, 1)\) we have \[ \abs{f_k(x_0) - f_k(1)} \convergesto{k\to \infty} 1 > \eps .\]
A non-equicontinuous sequence
E-LXY7N
- Area
- Complex Analysis
- Topics
- Counterexamples, Equicontinuity, Sequences of Functions
- Status
- draft