Let \(M\) be a manifold with boundary . Then the adjunction space \(M\cup_h M\) with the identity map \(h\colon \partial M\to \partial M\) is called double of \(M\) and denoted by \(D(M)\). That means we get the double of \(M\) by attaching two copies of \(M\) along the boundary.
Remarks
- According to (0x67bb6e48) \(D(M)\) is a manifold without boundary.
- Every \(n\)-manifold with boundary is homeomorphic to a closed subset of a \(n\)-manifold without boundary.
- Double of a connected manifold is connected.