The Unapologetic Mathematician

Mathematics for the interested outsider

The Implicit Function Theorem

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April 15, 2011 - Posted by | Differential Topology, Topology


  1. […] is basically the actual extension of the second part of the implicit function theorem to manifolds. Appropriately, then, we’ll let be the same inclusion into the first […]

    Pingback by Immersions are Locally Embeddings « The Unapologetic Mathematician | April 19, 2011 | Reply

  2. […] values are useful because of the generalization of the first part of the implicit function theorem: if is a regular value of , then is a topological manifold of dimension . Or, to put it another […]

    Pingback by Regular and Critical Points « The Unapologetic Mathematician | April 21, 2011 | Reply

  3. […] Armstrong: The Implicit Function Theorem, Immersions and Embeddings, Immersions are locally […]

    Pingback by Fourth Linkfest | April 23, 2011 | Reply

  4. (V,h) in the third paragraph must be a coordinate patch of \mathbb{R}^m instead of \mathbb{R}^n.

    Comment by Thomas (@Redfrettchen) | August 6, 2011 | Reply

  5. Thanks, Thomas; fixed.

    Comment by John Armstrong | August 6, 2011 | Reply

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