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$C^1$-homogeneous compacta in $\mathbb R^n$
are $C^1$-submanifolds of $\mathbb R^n$

Authors: Dusan Repovs, Arkadij B. Skopenkov and Evgenij V. Scepin
Journal: Proc. Amer. Math. Soc. 124 (1996), 1219-1226
MSC (1991): Primary 53A04, 54F65, 26A24; Secondary 26A03, 54F50, 26A16, 28A15
MathSciNet review: 1301046
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Dusan Repovs

Keywords: $C^1$-homogeneous compacta, $C^1$-submanifold of $\mathbb R^n$, Hilbert-Smith conjecture, LIP-homeomorphism, Lipschitz chart, almost everywhere differentiability
Received by editor(s): January 15, 1992
Received by editor(s) in revised form: September 15, 1994
Additional Notes: The first author was supported in part by the Ministry of Science and Technology of the Republic of Slovenia grant No. P1-0214-101-92.
Communicated by: James E. West
Article copyright: © Copyright 1996 American Mathematical Society

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