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## Main Question or Discussion Point

I try to solve the following problem: If S be submanifold of M and every smooth function f on S has a smooth extentsion to all of M, then S is properly embedded. [smooth means C-infinity].

I can show that S is embedded. What I need is to show either S is closed in M or the inclusion map is proper. If you have any suggestion please well come. Thank you in advance.

I can show that S is embedded. What I need is to show either S is closed in M or the inclusion map is proper. If you have any suggestion please well come. Thank you in advance.