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 \(\mathbb {R} ^{n}\).
Table of Contents
- Definition: Differentiable Manifold, Atlas
- Definition: \(C^n\) Differentiable Function
- Definition: Tangent Bundle
- Definition: Cotangent Bundle
- Definition: Section over a Base Space
- Definition: Differential Form of Degree k
Mentioned in:
Definitions: 1 2
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References
Adapted from CC BY-SA 3.0 Sources:
- Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück
