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
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 $\displaystyle (S^{n-1} \times S^{m-1} \times \{1\})/S^{n-1}$.