Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $g(x)=0$ for $x \in [0,1]^c$. Let $\mathcal{A} =\{ \phi_k: x \mapsto g(x-k) | k \in \mathbb{N} \}$ be a subset of $C([0,1])$. Why does the application of the Arzela-Ascoli theorem fail for $\mathcal{A}$ (w.r.t. $\| \cdot \|_{\sup})$?
2026-04-03 18:59:05.1775242745
Application of Arzela-Ascoli
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