From a certain topological viewpoint, a coffee-cup is the "same" as a donut.  That doesn't mean we can't distinguish between the two when we have breakfast, because there are physical consequences to the transformation from one to the other.  In the same way, saying that there is a topology-preserving transformation that sends "interior" to "exterior" of a sphere is non-controversial — but it doesn't mean that we can't distinguish interior from exterior because there are physically observable consequences to such a coordinate transformation.    22:06, Oct 22, 2004 (UTC)