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 $\\mathbb{R}$ -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.

单词	TopologicalManifold
释义	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 $\\mathbb{R}$ -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.
随便看	SimplePole simple pole SimplePredictableProcess simple predictable process SimpleRandomSample simple random sample SimpleRing simple ring SimpleRoot simple root SimpleSemigroup simple semigroup SimplestCommonEquationOfConics simplest common equation of conics SimpleTensor simple tensor SimpleTranscendentalFieldExtension simple transcendental field extension SimplexAlgorithm simplex algorithm SimplicialApproximation simplicial approximation SimplicialApproximationTheorem simplicial approximation theorem SimplicialComplex