Are two spaces manifolds if their product is a manifold? [duplicate]
Possible Duplicate:
Decomposition of a manifold
For topological spaces $X,Y$, if their product space $X \times Y$ is a manifold, is it necessarily that $X,Y$ are manifolds?
No. The dogbone space $D$ is a topological space that is not a manifold but $D \times \mathbb{R} \cong \mathbb{R}^4$.