Let \(C[0,1]\) be the set of continuous functions \(f:[0,1]\to\mathbb R\). Define \[ \rho(f,g)=\int_0^1|f(x)-g(x)|\,dx \] and \[ \mu(f,g)=\max_{x\in[0,1]}|f(x)-g(x)|. \] Both define metrics on \(C[0,1]\). Which metric induces the finer topology?
Compare the $L^1$ and uniform metric topologies on $C[0,1]$
P-WESTOP14-5
- Area
- Topology
- Seen at
- WESLEYAN
- Years
- 2014
- Status
- draft