TITLE: Boundary of product manifolds such as $S^2 \times \mathbb R$
QUESTION [7 upvotes]: Simple question but I am confused.
What is the boundary of $S^2\times\mathbb{R}$? Is it just $S^2$?
What would be the general way to evaluate the boundary of a product manifold?
Thanks for the replies!

REPLY [6 votes]: If you are interested in differentiable manifolds, a variation of what joriki said is still true. If $X$ is a manifold without boundary and $Y$, a manifold with boundary $\partial Y$, then $X\times Y$ is a manifold with boundary $X\times \partial Y$. For more details, you can look at many places, e.g. Guillemin and Pollack Differential Topology, Chapter 2.