MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

Decomposition of Rn with compact factor [closed]

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

-
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
show 4 more comments