Rich wrote: << . . . separability test seems to work if we allow spheres as separators (instead of just allowing planes).

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Yes -- the family F = {all spheres and planes in R^3} is large enough to separate any two circles in R^3 that don't link. By the way, F has a natural topology homeomorphic to a punctured P^4 (4-dimensional projective space minus a point). --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele