- #1
tronter
- 183
- 1
If f \cdot f and f \cdot f \cdot f is smooth, does it follow that f is smooth?
So does f \cdot f \in C^{\infty} \ \text{and} \ f \cdot f \cdot f \in C^{\infty} \Rightarrow f \in C^{\infty}?
Maybe we could generalize a bit more: Given that f^{n} , f^{n-1} \in C^{\infty} does it follow that f \in C^{\infty} (where f^n is the function raised to some power n)?
So does f \cdot f \in C^{\infty} \ \text{and} \ f \cdot f \cdot f \in C^{\infty} \Rightarrow f \in C^{\infty}?
Maybe we could generalize a bit more: Given that f^{n} , f^{n-1} \in C^{\infty} does it follow that f \in C^{\infty} (where f^n is the function raised to some power n)?
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