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
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Definitions: 1 2
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References
Adapted from CC BYSA 3.0 Sources:
 Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of OsnabrÃ¼ck