Open subsets of arbitrary subsets of manifolds

[mkoeppe]

Various places in the code assumed that the elements of the _supersets attribute of an open set are open, but this is not a guaranteed invariant.

We fix this by updating all loops over supersets that need to make this assumption to use a new generator function ManifoldSubset.open_supersets.

We also add the method ManifoldSubset.open_subset. It delegates to its base manifold's open_subset method, by passing a new optional parameter supersets to it.

Depends on #31674

CC: @mjungmath @egourgoulhon @tscrim

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: b35eca1

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/31677

[mkoeppe]

Branch: u/mkoeppe/open-subsets-of-arbitrary-subsets

[mkoeppe]

Commit: 4e63b30

[mkoeppe]

comment:2

Here's the beginning. To complete it, the remaining open_subset methods will need updating.

---

New commits:

1f6f295	TopologicalSubmanifold.open_subset: New
58110f2	TopologicalSubmanifold.open_subset: Fix docstring
d815b63	{DifferentiableSubmanifold,PseudoRiemannianSubmanifold}.open_subset: New
aac8835	{Topological,Differentiable,PseudoRiemannianSubmanifold}._repr_: Print subsets as subsets
004c23a	Add/update examples
ef1614a	Refactor Manifold.open_subset methods through new method _init_open_subset
265b0e2	TopologicalManifold._init_open_subset: Add docstring
4e63b30	WIP

[sagetrac-git]

Changed commit from 4e63b30 to 5623f49

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

a93f7ed	TopologicalSubmanifold._init_open_subset: Add docstring
58b43f7	DifferentiableManifold._init_open_subset: Add docstring
5623f49	WIP

[sagetrac-git]

Changed commit from 5623f49 to b35eca1

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

d542412	ManifoldSubset.open_supersets: New generator, use it to fix loops that assume open supersets
c821a75	{Topological,...}Manifold.open_subset: New optional parameter supersets
b35eca1	ManifoldSubset.{open_subset,_init_open_subset}: New

[egourgoulhon]

comment:6

LGTM. Thanks for this improvement!

[egourgoulhon]

Reviewer: Eric Gourgoulhon

[mkoeppe]

comment:8

Thanks for reviewing!

[vbraun]

Changed branch from u/mkoeppe/open-subsets-of-arbitrary-subsets to b35eca1