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Set of critical values is compact

Since both $M$ and $S^p$ are compact, you can choose finite atlases $\{\mathcal{U}_i\}$ and $\{\mathcal{V}_j\}$ for them, where each $\mathcal{U}_i$ is an open subset of $\mathbb{R}^n$ and each $\math …
Francesco Polizzi's user avatar