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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Dusan Repovs; Arkadij B. Skopenkov; 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: 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
Affiliation: Steklov Mathematical Institute, Russian Academy of Sciences, 42 Vavilova Street, 117966 Moscow GSP-1, Russia
Address at time of publication: Institute for Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 64, Ljubljana 61111, Slovenia
Email: dusan.repovs@uni-lj.si

Arkadij B. Skopenkov
Affiliation: Steklov Mathematical Institute, Russian Academy of Sciences, 42 Vavilova Street, 117966 Moscow GSP-1, Russia

Evgenij V. Scepin
Affiliation: Steklov Mathematical Institute, Russian Academy of Sciences, 42 Vavilova Street, 117966 Moscow GSP-1, Russia

DOI: 10.1090/S0002-9939-96-03157-7
PII: S 0002-9939(96)03157-7
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
Copyright of article: Copyright 1996, American Mathematical Society

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