topological manifold
The definition given in the manifold
article is in fact the definition of topological manifold. If we change it to allow only smooth (differentiable
) transition (maximal rank) functions
, then we speak of a smooth manifold.
Or if we take real analytic function
as the transition ones we get -analytic manifolds.
One must emphasize that the invariant number appearing in the definition there is the dimension of the manifold which is also the dimension of the tangent space at a point, in a smooth manifold.
| Title | topological manifold |
|---|---|
| Canonical name | TopologicalManifold |
| Date of creation | 2013-03-22 16:02:05 |
| Last modified on | 2013-03-22 16:02:05 |
| Owner | juanman (12619) |
| Last modified by | juanman (12619) |
| Numerical id | 7 |
| Author | juanman (12619) |
| Entry type | Definition |
| Classification | msc 53-00 |
| Classification | msc 57R50 |
| Related topic | Manifold |
| Defines | topological manifold |