1. ## Sphere...

Hi - please delete this thread. I have solved the question myself & without the post made by aiw.

Therefore this post will be of no use to anyone else - please could you delete it.

Thank you x

2. Originally Posted by TTB
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.
Isn't join of the spheres $\displaystyle S^{n-1}$ and $\displaystyle S^{m-1}$ is the sphere $\displaystyle S^{n+m-1}$? By the definition of join, you have an embedding $\displaystyle f:S^{n-1} \rightarrow S^{n+m-1}$ and $\displaystyle g:S^{m-1} \rightarrow S^{n+m-1}$, since $\displaystyle S^{n-1}$ can be embedded into $\displaystyle (S^{n-1} \times S^{m-1} \times \{0\})/S^{m-1}$ and $\displaystyle S^{m-1}$ can be embedded into $\displaystyle (S^{n-1} \times S^{m-1} \times \{1\})/S^{n-1}$.

3. It's ok, I think I've sorted it out now.

Thanks anyway. x