# 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.

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 |