***Spheres Rule*** (for separating unlinked circles in 3-space) Rich wrote: << (b) Fred's separability test seems to work if we allow spheres as separators (instead of just allowing planes).

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As I previously posted, the family of all planes and spheres is sufficient to separate any two unlinked circles in 3-space. (This after initially believing that spheres alone are not sufficient). But Fred kindly mentioned a proof he has that spheres alone are sufficient. And now I see that -- since the family of planes and spheres is sufficient -- it follows that spheres alone must be sufficient. (For, any plane can be approximated arbitrarily well, in an arbitrarily large finite region of space, by spheres.) Finally, this might be what Rich was saying all along. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele