Decomposition of Rn with compact factor

Decomposition of Rn with compact factor [closed]

can Rn be diffeomorphic to a product manifold NxM, with N compact d-manifold d>1?

edited Dec 16 2011 at 21:18

asked Dec 16 2011 at 21:05

Sure, take $N$ to be a point. – Qiaochu Yuan Dec 16 2011 at 21:07

In what way does it not answer your question? – Mariano Suárez-Alvarez Dec 16 2011 at 21:14

Are you asking for a diffeomorphism $\mathbb{R}^n \to N \times M$ with $N$ a compact manifold (which I don't think is appropriate for this site), or are you asking for a homeomorphism $\mathbb{R}^n \to N \times M$ with $N$ a compact topological space (which I think is a fine question for this site)? – Richard Kent Dec 16 2011 at 21:26

Look at Kunneth theorem over Z/2Z? HW question? – Daniel Pomerleano Dec 16 2011 at 21:27

Homework, voting to close. – Igor Rivin Dec 16 2011 at 21:28

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closed as too localized by Igor Rivin, Dan Petersen, Ryan Budney, Yemon Choi, Andy Putman Dec 16 2011 at 23:03

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