Changes between Version 1 and Version 2 of Ticket #31241, comment 29
- Timestamp:
- 06/02/21 22:32:42 (6 months ago)
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Ticket #31241, comment 29
v1 v2 6 6 To impose a differentiable structure, we add an additional atlas, namely the maximal ''differentiable'' atlas. So in a way, we can say that a differentiable manifold is endowed with two atlases. However, it turns out that the topological atlas is not needed because it can be recovered from the differentiable atlas. 7 7 8 Now, when we apply the forgetful functor, we simply forget about the differentiable atlas, and what remains is maximal ''topological'' atlas.8 Now, when we apply the forgetful functor, we simply forget about the differentiable atlas, and what remains is the maximal ''topological'' atlas. 9 9 10 10 So you were right when you said "the atlas does not change". I suppose I was just extremely sloppy here. Does that resolve some things?
