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Remove a critical point and what happensPosted by Mike2 on June 18, 2003 at 09:27:19: I'm wondering what happens when a critical point is removed from a manifold. As I recall, critical points result in every partial derivative being zeros so that there can be no basis vectors to describe anything at that point. So I wonder what happens when the critical point is removed or disallowed in a manifold. Does the resulting manifold necessarily have a boundary around the critical point? For example, a sphere with a hole in it? Thanks.
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