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

DOI10.1090/S0002-9939-96-03157-7zbMath0863.53004OpenAlexW1598845174MaRDI QIDQ4875578

Dušan D. Repovš, Evgeny V. Shchepin, Arkadij B. Skopenkov

Publication date: 28 May 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-96-03157-7

zbMATH Keywords

compact subset\(C^ 1\)-homogeneous\(C^ 1\)-submanifold

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Topological characterizations of particular spaces (54F65) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Global submanifolds (53C40) Topological spaces of dimension (leq 1); curves, dendrites (54F50) Abstract differentiation theory, differentiation of set functions (28A15)

Related Items (12)

The work of Federico Rodriguez Hertz on ergodicity of dynamical systems ⋮ On a theorem of Shchepin and Repovš concerning the smoothness of compacta ⋮ A characterization of submanifolds by a homogeneity condition ⋮ Structure of accessibility classes ⋮ NOWHERE‐ANALYTIC SMOOTH CURVES WITH NON‐TRIVIAL ANALYTIC ISOTROPY ⋮ Geodesic manifolds with a transitive subset of smooth biLipschitz maps ⋮ Cantor sets are not tangent homogeneous ⋮ Holomorphically homogeneous real hypersurfaces in $\mathbb {C}^3$ ⋮ Hausdorff dimension and the dynamics of diffeomorphisms ⋮ On smoothness of compacta ⋮ Absolute continuity, Lyapunov exponents, and rigidity II: systems with compact center leaves ⋮ Ergodicity and partial hyperbolicity on the 3-torus

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• Locally compact groups of differentiable transformations
• The Bitangent Sphere Problem
• Spheres Uniformly Wedged Between Balls are Tame in E 3
• A Surface in E 3 is Tame if it has Round Tangent Balls

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