Let X be a compnact subset of the n-1 sphere in R^n space & Y a compact sunset of the m-1 sphere in R^m space.

Then I need to prove that f:X*Y ---> R^n x R^m given by f(x,y,t) = (x(1-t),yt) is an embedding, where * denoted the "join" of 2 spaces. []Error

I think I've got it to the point (through some cheeky theorems involving compactness, hausdorffness, etc) that i only need to show that f is injective & continuous. Any ideas on how to do this?

Or am I going off in completely the wrong direction?

Thanks x