How do I show that the join [
http://en.wikipedia.org/wiki/Join_(topology) Intuitively it is formed by taking the disjoint union of the two spaces and attaching a line segment joining every point in A to every point in B] of the spheres S^n-1 and S^m-1 is the sphere S^(m+n)?
PS - I have an embedding from the join of a copact subset of S^n-1 & a compact snset of S^m-1 to the m+n-dim Euclidean plane, but not sure if that is needed for the above problem or if so how to use it.