# The Unapologetic Mathematician

## The Implicit Function Theorem

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 […]

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