In the context of manifold with boundary, closed manifold, compact manifold I have the following question in my mind : Let $M$ be a compact manifold with non-empty boundary $\partial M$. Then $\operatorname{int}( M) =M-\partial M$ is a manifold without boundary. Can $\operatorname{int}(M)$ be a COMPACT manifold without boundary?
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HINT: Can open set be compact? (I am assuming that you have not in mind a compact manifold minus its boundary, because there are many affirmative examples, in particular closed balls).
Przemysław Scherwentke
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Oh yes I understand, asked a stupid question. – Bingo Dec 12 '14 at 07:36