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 $ℝ$-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