# Thread: Norm and Uniform Convergence

1. ## Norm and Uniform Convergence

Any hints on how to approach these two questions?

Thanks a lot

2. For a) just observe that A is compact.

b) is immediate from the very definition. Uniform convergence to f certainly is equivalent to the convergence to 0 of

$\displaystyle \{\sup\|f_k(x)-f(x)\|: x\in A\}$