Topological Join of Unit Balls I have seen that apparently one has for spheres that $S^n*S^m=S^{n+m+1}$. Is there a similar result for unit balls?
Thank you.

if you take simplexes instead of balls, it's easy to see that $\Delta^m*\Delta^n=\Delta^{m+n+1}$. one can prove it by induction, using $\Delta^m*pt=\Delta^{m+1}$ and the fact that join operation is associative.
