Pullbacks (preimages) of manifold subsets under continuous maps

[mkoeppe]

Similar to #31653, given a continuous map \Phi: N -> M and a manifold subset S of M, we define the pullback (preimage) of S as the subset of N of points p with \Phi(p) in S.

Given a real scalar field Phi: N -> R and a RealSet S, we define the pullback in the same way.

Also, we view a chart C as a continuous function Phi: C.domain() -> R^n and allow pulling back any subset of R^n (an object with a __contains__ method; for example polyhedra, lattices, linear subspaces, tensor modules) by it as well.

In all cases, because Phi is continuous, topological closures/interiors pull back.

An application is in #31981.

Depends on #31883
Depends on #31904
Depends on #31653
Depends on #31916
Depends on #31644
Depends on #31959
Depends on #31990
Depends on #21243

CC: @egourgoulhon @tscrim @mjungmath

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: 4558e26

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/31688

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,2 +1,7 @@
 Similar to #31653, given a continuous map `\Phi: N -> M` and a manifold subset `S` of `M`, we define the pullback (preimage) of `S` as the subset of `N` of points `p` with `\Phi(p)` in `S`.
 
+Given a real scalar field `Phi: N -> R` and a RealSet `S`, we define the pullback in the same way.
+
+In both cases, because `Phi` is continuous, topological closures/interiors pull back.
+
+

[mkoeppe]

Dependencies: #31883

[mkoeppe]

Branch: u/mkoeppe/pullbacks_of_manifold_subsets_under_continuous_maps

[sagetrac-git]

Commit: 941001b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

1942c71	ScalarField.codomain: New, put scalar fields in category of continuous maps
8829d72	Merge #31883
941001b	ManifoldSubsetPullback: More WIP

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,6 +1,6 @@
 Similar to #31653, given a continuous map `\Phi: N -> M` and a manifold subset `S` of `M`, we define the pullback (preimage) of `S` as the subset of `N` of points `p` with `\Phi(p)` in `S`.
 
-Given a real scalar field `Phi: N -> R` and a RealSet `S`, we define the pullback in the same way.
+Given a real scalar field `Phi: N -> R` and a `RealSet` `S`, we define the pullback in the same way.
 
 In both cases, because `Phi` is continuous, topological closures/interiors pull back.
 

[sagetrac-git]

Changed commit from 941001b to 90f763f

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

90f763f

ManifoldSubsetPullback.__contains__: New

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

ff34765	ManifoldSubsetPullback: In `__classcall_private__`, make immutable copies of the maps
b8dadf3	ScalarField.pullback, ContinuousMap.pullback: New

[sagetrac-git]

Changed commit from 90f763f to b8dadf3

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

5abb86d

ManifoldSubsetPullback: More WIP

[sagetrac-git]

Changed commit from b8dadf3 to 5abb86d

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

e597e6d

ManifoldSubsetPullback: Allow pulling back by charts, pulling back polyehdra

[sagetrac-git]

Changed commit from 5abb86d to e597e6d