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Re: Remove a critical point and what happensPosted by DickT on June 19, 2003 at 17:34:09: In Reply to: Re: Remove a critical point and what happens posted by Mike2 on June 19, 2003 at 09:37:18: Mike, Mathematicians are quite used to these matters in complex function theory. A complex function is defined over the plane, and it can have a pole - a kind of singularity - at some point of the plane. Then it is analytic (nice) in the compement of that point - an open subset of the plane. But theorems commonly approximation that by drawing a small closed surve around the point and deleting the interior. You need the curve in the remainder because in theorems you want to integrate around it. Since the function is known to be analytic in the complemnent of the point, and the closed curve lies entirely in that complement, therefore the function is analytic on the curve. This is the basis for what I said about singularities in spacetime. The cosmic censorship hypothesis says that every singularity is hidden behind a horizon. Physics works on the horizon which is in the complement of the singularity. So you can (and many do) treat the physics of normal space with horizons limiting it. Regards, Follow Ups: (Reload page to see most recent)
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