topological manifold

The definition given in the manifoldMathworldPlanetmath article is in fact the definition of topological manifold. If we change it to allow only smooth (differentiableMathworldPlanetmathPlanetmath) transition (maximal rank) functionsMathworldPlanetmath, then we speak of a smooth manifold. Or if we take real analytic functionMathworldPlanetmath as the transition ones we get -analytic manifolds.

One must emphasize that the invariant number n 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