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Let $M$ be a compact submanifold of $R^2$ of dimension $2$, with boundary (for instance: a compact disc in which small disjoint compact discs have been cut off). By drawing pictures, it seems that the boundary of $M$ can be decomposed in a finite union of Jordan curves. Is there a formal proof for that?

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  • $\begingroup$ "Let $M$ be a compact submanifold of $R^2$ of dimension $2$". Are you sure ($2$ and $2$)? $\endgroup$
    – user91684
    Apr 9, 2016 at 18:20

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