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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?

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    Also related: http://math.stacke$x$change.com/q/169195/53632012-08-02

1 Answers 1

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