1. The problem statement, all variables and given/known dataLet C([0,1]) be the metric space of continuous functions on the interval [0,1] with distance = max of x over [0,1] of |f(x)-g(x)|. Is the ball of radius 1 centered around f(x) = 0 compact? 3. The attempt at a solutionI originally thought it was but now I believe that it is not compact. I'm not sure how to prove it though. I know I can use either sequential convergence or show that it isn't totally bounded, but this is where I get stuck. I know the ball has all continuous functions s.t. |f(x)| < 1. How can I go about showing it isnt sequentially compact or that it isnt totally bounded? Anyone can put me in the right direction?