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