Theorems in differential topology

Whitney immersion theorem

In differential topology, the Whitney immersion theorem (named after Hassler Whitney) states that for , any smooth -dimensional manifold (required also to be Hausdorff and second-countable) has a one-to-one immersion in Euclidean -space, and a (not necessarily one-to-one) immersion in -space. Similarly, every smooth -dimensional manifold can be immersed in the -dimensional sphere (this removes the constraint). The weak version, for , is due to transversality (general position, dimension counting): two m-dimensional manifolds in intersect generically in a 0-dimensional space. (Wikipedia).

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From playlist Mathematics

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Introduction to Homogeneous Differential Equations

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From playlist Differential Equations

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From playlist Bernoulli Differential Equations

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From playlist Mathematics

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From playlist Mathematics

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From playlist Discrete Differential Geometry - CMU 15-458/858

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From playlist Vector Calculus

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From playlist Discrete Differential Geometry - CMU 15-458/858

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From playlist Differential Equations

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From playlist Multivariable calculus

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From playlist Partial differential equations

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From playlist BOURBAKI - 2019

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From playlist Workshop: Topology of Data in Rome

Related pages

Manifold | Transversality (mathematics) | General position | Whitney embedding theorem | Hassler Whitney | Euclidean space | Hausdorff space | Cobordism | Differential topology | Immersion (mathematics)