Does C^1-structures ensure structures of higher regularity?

Does the existence of a \(C^1\)-structure on a manifold \(M\) implies the existence of structures with higher regularity? The answer is yes:

If \( M \) has a \( C^1 \)-structure, then \( M \) has a smooth atlas ( Whitney, 1936).
If \( M \) has a \( C^1 \)-structure, then \( M \) has a real analytic atlas (Narsinhan, 1971).

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