Let $K\subset \mathbb{R}$ a compact set. Build continuos functions of compact support $\varphi_n$ so that $0\leq \varphi_n\leq 1$, $\varphi_n|_K=1$ and $\varphi_n(x)\to 1_K(x)$ for all $x\in\mathbb{R}$.
2026-03-30 20:54:19.1774904059
Continuos functions of compact support so that $\varphi_n(x)\to 1_K(x)$ for all $x\in\mathbb{R}$.
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