Definition: Manifold

A topological Hausdorff space \(M\) is called an \(n\)-dimensional (topological) manifold, if there exist an open cover \[M=\bigcup _{i\in I}U_{i}\] with the property that each \(U_{i}\) is homeomorphic to an open subset of the \(n\)-dimensional metric space or real numbers \(\mathbb {R} ^{n}\).

  1. Definition: Differentiable Manifold, Atlas
  2. Definition: \(C^n\) Differentiable Function
  3. Definition: Tangent Bundle
  4. Definition: Cotangent Bundle
  5. Definition: Section over a Base Space
  6. Definition: Differential Form of Degree k

Definitions: 1 2

Thank you to the contributors under CC BY-SA 4.0!



Adapted from CC BY-SA 3.0 Sources:

  1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück