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Results tagged with surfaces
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user 40804
A surface is a two-dimensional topological manifold. The term can also be used to describe a smooth surface, depending on the context.
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Topology change induced by small perturbation
The formal statement you are thinking of when you assert "The topology changes only when..." is Ehresmann's theorem: a proper smooth submersion is a fiber bundle, and hence all fibers are diffeomorphi …
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