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Results tagged with surfaces
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user 50614
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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Problem of Thickening an Arc in a Topological $ 2 $-Manifold
Let $ M $ be a topological $ 2 $-manifold (possibly with boundary), $ C $ an arc in the interior of $ M $ (i.e., an injective continuous function from $ [- 1,1] $ into $ \operatorname{Int}(M) $), and …
- 1,396
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A Jordan Separation Theorem for Polyhedral Surfaces
Then one can apply the Classification Theorem for Surfaces to prove that it must be homeomorphic to either a $ 2 $-sphere or a finite connected sum of $ 2 $-tori. …
- 1,396