Connected sum of compact manifolds is compact

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Suppose n is a natural number and M_1, M_2 are Compact connected manifold (?)s of dimension n. In other words, each of M_1 and M_2 is both a Compact manifold (?) (and in particular, a Compact space (?)) and a Connected manifold (?) (and in particular, a Path-connected space (?)).

Then, the Connected sum (?) M_1 \# M_2 is also a compact manifold.

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