𝐶¹-homogeneous compacta in ℝⁿ are ℂ¹-submanifolds of ℝⁿ

Repovs, Dusan; Skopenkov, Arkadij; Scepin, Evgenij

doi:10.1090/S0002-9939-96-03157-7

$C^1$-homogeneous compacta in $\mathbb {R}^n$ are $C^1$-submanifolds of $\mathbb {R}^n$
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by Dusan Repovs, Arkadij B. Skopenkov and Evgenij V. Scepin PDF

Proc. Amer. Math. Soc. 124 (1996), 1219-1226 Request permission

Abstract:

We give the characterization of $C^1$-homogeneous compacta in $\mathbb R^n$: Let $K$ be a locally compact (possibly nonclosed) subset of $\mathbb R^n$. Then $K$ is $C^1$-homogeneous if and only if $K$ is a $C^1$-submanifold of $\mathbb R^n$.

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