$C^1$-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 $\mathbb R^n$.References
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Additional Information
- Dusan Repovs
- MR Author ID: 147135
- ORCID: 0000-0002-6643-1271
- Email: dusan.repovs@uni-lj.si
- 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 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1219-1226
- MSC (1991): Primary 53A04, 54F65, 26A24; Secondary 26A03, 54F50, 26A16, 28A15
- DOI: https://doi.org/10.1090/S0002-9939-96-03157-7
- MathSciNet review: 1301046