(July 16, 2012 at 6:47 pm)CliveStaples Wrote:(July 16, 2012 at 2:37 pm)jonb Wrote: Is the same true for a sphere enclosing a sphere? At what point does the surface of the object become the object?
I'm not sure what you mean by "a sphere enclosing a sphere." Suppose that S1 is a sphere of radius r1, and S2 a sphere of radius r2. If r2>r1, and S1 and S2 share the same center, then S2 encloses S1. This doesn't change S1's topology or S2's topology.
Or do you mean the surface enclosing the region 'between' the spheres?
A space of zero is enclosed by shell with no or one hole in it of zero size that shell is a sphere, the same shell with two holes is a tours since the holes are of zero magnitude how would you detect them?
I have a space of zero size what shape is it?