Let $M$ be a k-dim. $C^1$-Manifold of $\mathbb{R}^n$ and $\phi:\mathbb{R}^n \rightarrow \mathbb{R}^n$ a diffeomorphism, proofe $\phi(M)$ is a manifold

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score 46 · Answer 15 · 2026-03-29 10:08:50

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For any Cantor set $C \subset R^n$ there exists a submanifold $M \subset R^{n+1}$ such that $M \cap (R^n \times \{0\}) = C$

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