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I need to show if $M \times \mathbb{R}^{n}$ is orientable than so is $M$, where $M$ is connected manifold. $R^{n}$ has standard orientation (determined by standard basis ) and by the assumption $M \times \mathbb{R}^{n}$ also orienatable, so how to show that $M$ is orientable?

cactus
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    What is your definition of Orientation ?http://math.stackexchange.com/questions/1055302/m-times-n-orientable-if-and-only-if-m-n-orientableis May be Helpful: – Arpit Kansal Mar 21 '15 at 10:57
  • A manifold is orientable if it has an orientable atlas – cactus Mar 21 '15 at 11:00
  • This has been solved here: http://math.stackexchange.com/questions/550426/product-of-manifolds-orientability/1110566#1110566 – Jesus RS Mar 21 '15 at 22:36

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