C[0,1] is not a metric space
Show that there is no metric 
on ![C[0,1]](/cz/latexrender/pictures/3db697426056e27680c2e275d81fb9cf.png "C[0,1]")
such that pointwise convergence and convergence in the metric coincide.
Possibly relevant posts:
- Pointwise convergence implies weak convergence (9/26/2008)
- Geodesics and Metrics (4/22/2005)
- Approximate Identities (7/2/2005)