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| Authors: | Dusan Repovs Arkadij B Skopenkov Evgenij V Scepin |
| Institution: | Steklov Mathematical Institute, Russian Academy of Sciences, 42 Vavilova Street, 117966 Moscow GSP-1, Russia ; Steklov Mathematical Institute, Russian Academy of Sciences, 42 Vavilova Street, 117966 Moscow GSP-1, Russia Evgenij V. Scepin ; Steklov Mathematical Institute, Russian Academy of Sciences, 42 Vavilova Street, 117966 Moscow GSP-1, Russia |
| Abstract: | We give the characterization of  -homogeneous compacta in  : Let  be a locally compact (possibly nonclosed) subset of  . Then  is  -homogeneous if and only if  is a  -submanifold of  . |
| Keywords: | $C^1$-homogeneous compacta $C^1$-submanifold of $\mathbb R^n$ Hilbert-Smith conjecture LIP-homeomorphism Lipschitz chart almost everywhere differentiability |
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