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?
Tell me more
×
Mathematics Stack Exchange is a question and answer site for
people studying math at any level and professionals in related fields. It's 100% free, no registration required.
|
|
|||
|
marked as duplicate by t.b., Nate Eldredge, Jonas Teuwen, Henning Makholm, Davide Giraudo Aug 2 '12 at 22:32
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
|
No. The dogbone space $D$ is a topological space that is not a manifold but $D \times \mathbb{R} \cong \mathbb{R}^4$. |
|||
|
|
