Changes between Version 1 and Version 2 of Ticket #31241, comment 22


Ignore:
Timestamp:
06/01/21 08:50:20 (6 months ago)
Author:
gh-mjungmath
Comment:

Legend:

Unmodified
Added
Removed
Modified
  • Ticket #31241, comment 22

    v1 v2  
    22> As I mentioned in #31877, the manifold is not as special as you want it to be. It can be provided more information, but it is not something that is mutable. Subsequently, you have genuinely different objects for topological and differentiable on the same underlying set if you have different maximal atlases. Applying the forgetful functor, you would have the ''same'' maximal atlas, which means the differentiable structure would still be there.
    33
    4 Sure, starting with a differential manifold and applying the forgetful functor to it, a new instance must be constructed, particularly an instance of `TopologicalManifold`. It should come with the "same" charts (different instances of course). Then you can add new charts dynamically, e.g. continuous but not differentiable, to the implementation. This is where the dynamic nature of manifolds comes into play.
     4Sure, starting with a differential manifold and applying the forgetful functor to it, a new instance must be constructed, particularly an instance of `TopologicalManifold`. It should come with the "same" charts (different instances of course). Then you can add new charts dynamically, e.g. continuous but not differentiable, to the implementation. This is where the dynamical nature of manifolds comes into play.
    55
    66That is at least how I would think the forgetful functor might be used in this case.