# Connected sum of compact manifolds is compact

From Topospaces

## Statement

Suppose is a natural number and are Compact connected manifold (?)s of dimension . In other words, each of and 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 (?) is also a compact manifold.