Theorem 1.6.1 (Arzela-Ascoli).label Let $K \subset \Omega$, then $K$ is compact if and only if the following holds:
- (1)
$\pi_{0}(K)$ is precompact.
- (2)
For each $N \in \nat$,
\[\lim_{\delta \to 0}\sup_{\omega \in K}V_{\delta, N}(\omega) = 0\]
Theorem 1.6.1 (Arzela-Ascoli).label Let $K \subset \Omega$, then $K$ is compact if and only if the following holds:
$\pi_{0}(K)$ is precompact.
For each $N \in \nat$,