Produce a sequence that is uniformly bounded but not equicontinuous.
Solution
\(f_k(x) = (\sin k x)\) is uniformly bounded but not equicontinuous on \((0, 1)\) since it has no convergent subsequence on any compact subset.
Uniformly bounded but not equicontinuous
E-YFL4K
- Area
- Complex Analysis
- Topics
- Counterexamples, Equicontinuity, Sequences of Functions
- Status
- draft