If $A=\{f\in C[0, 1]: \int^1_0|f(x)|^2\,dx\leq1\}$ and metric $d(f, g)$ is $(\int^1_0|f(x)-g(x)|^2dx)^\frac{1}{2}$. Is $A$ totally bounded? I know $A$ is clearly bounded since $d(f, 0)\leq 1$ under the chosen metric function. Any hint?
2026-04-28 21:47:27.1777412847
Is this a totally bounded set in the space of continuous functions?
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