Frederic Schuller on Topological Manifolds and Manifold Bundles

22:54 Bundles.

36:52 Sections. 

52:44 Bundle Isomorphisms. 

1:09:25 Pullback of a Bundle. 

1:18:04 Viewing Manifolds from Charts and C⁰-compatibility. 

Differentiable structures

9:23 See Cauchy–Riemann equations. 

1:05:52 Amusing observation about the number of possible smooth manifolds you can construct on a four-dimensional compact topological manifold such as Einstein's space-time. 

Tensor spaces over a ring: 

45:33 Proof of the Hamel Basis Theorem for a division module. 

1:33:52 Because the smooth functions on a manifold are not a division ring, one cannot think of tensor fields in terms of their component functions. Locally, this is always possible, but not globally. 

See Frederic Schuller on Metric and Topological Spaces and Tensor Fields and Simplicial Complexes. 

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