[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.


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