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Approximation of $C^1$-smooth equivariant maps by infinitely smooth ones

Let $M,N$ be smooth closed manifolds acted by a finite group $G$. Let $f\colon M\to N$ be a $C^1$-smooth $G$-equivariant map. Is it true that for any $\varepsilon>0$ there exists a $C^\infty$-...
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