I notice that $T^2=S^1\times S^1$ can be embedded in $\mathbb{R}^3$ as a hypersurface (submnaifolds of codimension 1). 


In general, 


(1). could the product of spheres $S^{m\_1}\times\cdots\times S^{m\_n}$ be embedded in Euclidean space as a hypersurface?


(2). could $T^n=\prod\_n S^{1}$ be embedded in Euclidean space as a hypersurface?


(3). could $S^m\times S^n$ be embedded in Euclidean space as a hypersurface?



embeddings of product of spheres in Euclidean spaces
This is [asked on MSE](https://math.stackexchange.com/questions/161293/product-of-spheres-embeds-in-euclidean-space-of-1-dimension-higher), and answered (see [Jim Belk's answer](https://math.stackexchange.com/a/161313), which is **NOT** the accepted answer).


