I found the relation between homeomorphic spaces - the slices have no encapsulated hole. This I believe solves PC, although I will be among the first to admit that the maths needs to be made presentable. Anyway, if anyone would like to publish this (plus other emials) as a proof, please contact me. Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com