[Intro to Topology] Verify if $K$ is compact

Consider $C[0, 1]$ with the norm $||f||$ =$\int_{0}^{1}|f(x)|dx$. Verify if the set $K = \{f ? C[0, 1] : f(0) = 0 = f(1)  and  ||f|| = 1\}$ is compact.

We were just introduced to compact metric spaces, so we don't have much beyond the definitions by open coverages and sequeneces.

Answer

Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
The answer is accepted.