TITLE: Are two spaces manifolds if their product is a manifold?
QUESTION [11 upvotes]: 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?

REPLY [11 votes]: No. The dogbone space $D$ is a topological space that is not a manifold but $D \times \mathbb{R} \cong \mathbb{R}^4$.