Are two spaces manifolds if their product is a manifold?

Question

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?

Answer 1

No. The dogbone space $D$ is a topological space that is not a manifold but $D \times \mathbb{R} \cong \mathbb{R}^4$.