Topological closure of manifold subsets, methods ManifoldSubset.closure, is_closed, declare_closed #31644

mkoeppe · 2021-04-10T23:45:40Z

We define a subclass of ManifoldSubset whose instances represents the topological closure of given subset in the manifold.

Subsets provide a method closure to construct it. When the subset is already closed, as detected by the new method is_closed, it just returns the input.

We also add a method declare_closed. It just sets up an open disjoint union with an open complement. (This is exactly what is_closed tests.)

The purpose of this is to build a connection of manifolds to cell complexes and convex polyhedra: In a separate ticket, we will define embedded submanifolds of euclidean spaces that arise as interiors of polyhedra or relative interiors of their faces.

Depends on #31763
Depends on #31798

CC: @egourgoulhon @tscrim @yuan-zhou @mjungmath

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: 9abc617

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/31644

The text was updated successfully, but these errors were encountered:

mjungmath · 2021-04-10T23:56:08Z

comment:1

That sounds extremely interesting!

Btw: Do you really mean cell complexes or rather simplicial complexes?

mkoeppe · 2021-04-11T01:09:53Z

comment:2

Simplicial is too narrow - that would not be enough (without triangulating) to represent general convex polyhedra and their boundary structure. So need something slightly more general.

mkoeppe · 2021-04-11T03:04:00Z

Branch: u/mkoeppe/topological_closure_of_embedded_submanifolds

mkoeppe · 2021-04-11T03:04:27Z

Author: Matthias Koeppe, ...

mkoeppe · 2021-04-11T03:04:27Z

Commit: 331aa59

mkoeppe · 2021-04-11T03:04:27Z

New commits:

`331aa59`	`sage.manifolds.closure_topological_submanifold, TopologicalSubmanifold.closure: New`

mkoeppe · 2021-04-11T03:23:34Z

comment:5

Here's a beginning.

Currently, is there already a way to get the image of the embedding of the submanifold in the ambient manifold as a "subset"?

mjungmath · 2021-04-11T09:17:26Z

comment:6

Replying to @mkoeppe:

New commits:

`331aa59`	`sage.manifolds.closure_topological_submanifold, TopologicalSubmanifold.closure: New`

Looks already nice!

Replying to @mkoeppe:

Simplicial is too narrow - that would not be enough (without triangulating) to represent general convex polyhedra and their boundary structure. So need something slightly more general.

Right, the cube is already a counter-example.

Replying to @mkoeppe:

Here's a beginning.

Currently, is there already a way to get the image of the embedding of the submanifold in the ambient manifold as a "subset"?

No, I don't think so.

egourgoulhon · 2021-04-11T10:20:11Z

comment:7

Replying to @mjungmath:

Replying to @mkoeppe:

Here's a beginning.

Currently, is there already a way to get the image of the embedding of the submanifold in the ambient manifold as a "subset"?

No, I don't think so.

I confirm; more generally, there is no such functionality for continuous maps.

mjungmath · 2021-04-11T13:12:11Z

comment:8

Speaking of boundary; I think we should slowly but surely consider to introduce manifolds with boundary...

egourgoulhon · 2021-04-11T13:33:14Z

comment:9

Replying to @mjungmath:

Speaking of boundary; I think we should slowly but surely consider to introduce manifolds with boundary...

Indeed. There is even some demand for it: https://ask.sagemath.org/question/56532/.

mkoeppe · 2021-04-11T15:49:41Z

Dependencies: #31653

mkoeppe · 2021-04-11T15:50:22Z

comment:11

Replying to @egourgoulhon:

Replying to @mjungmath:

Replying to @mkoeppe:

Currently, is there already a way to get the image of the embedding of the submanifold in the ambient manifold as a "subset"?

No, I don't think so.

I confirm; more generally, there is no such functionality for continuous maps.

OK, I have opened #31653 for this

sagetrac-git · 2021-04-11T16:29:25Z

Changed commit from 331aa59 to 0579188

sagetrac-git · 2021-04-11T16:29:25Z

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

`0579188`	`Fixup`

mkoeppe · 2021-04-11T21:58:52Z

Work Issues: redo on top of #31653

sagetrac-git · 2021-04-29T21:11:28Z

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

`26c7e56`	`src/sage/manifolds/continuous_map_image.py: Update doctests`
`3e273bb`	`TopologicalSubmanifold.as_subset: New`
`9726d36`	`Docstring work`
`19762ae`	`ImageManifoldSubset: New parameter domain_subset, use it in ContinuousMap.image`
`964f9f7`	`src/sage/manifolds/continuous_map.py: Update copyright`
`e711215`	`src/sage/manifolds/continuous_map_image.py: Add tests`
`0f3e36d`	`Link in documentation of sage.manifolds.continuous_map_image`
`218117b`	`sage.manifolds.closure_topological_submanifold, TopologicalSubmanifold.closure: New`
`3b3662e`	`Fixup`
`0666fae`	`Change to ClosureOfManifoldSubset`

sagetrac-git · 2021-04-29T21:11:28Z

Changed commit from 0579188 to 0666fae

sagetrac-git · 2021-04-30T04:45:26Z

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

`426e087`	`ManifoldSubset.declare_{sub,super}set: New`
`72294f0`	`ManifoldSubset.closure: New`

sagetrac-git · 2021-04-30T04:45:26Z

Changed commit from 0666fae to 72294f0

mkoeppe · 2021-04-30T04:51:29Z

Changed author from Matthias Koeppe, ... to Matthias Koeppe

mkoeppe · 2021-04-30T04:51:29Z

Changed work issues from redo on top of #31653 to none

sagetrac-git · 2021-05-19T15:38:00Z

Changed commit from ac53984 to 60505b0

mjungmath · 2021-05-30T09:40:02Z

comment:35

One doctest has failed. Is that related to this ticket?

mkoeppe · 2021-05-30T16:54:22Z

comment:36

No, it's unrelated, see #31848

egourgoulhon · 2021-06-02T15:03:36Z

comment:37

Looks nice!

There is a spurious line feed in the html documentation of ManifoldSubsetClosure, which can be fixed with

     - ``name`` -- (default: computed from the name of the subset)
-       string; name (symbol) given to the closure
+      string; name (symbol) given to the closure

Besides, there should be some EXAMPLES section in the main docstring of ManifoldSubsetClosure, and the latter should start with r""", instead of """, I think.

sagetrac-git · 2021-06-02T16:58:27Z

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

`b9909c0`	`ManifoldSubsetClosure: Add examples, fix docstring markup`

sagetrac-git · 2021-06-02T16:58:27Z

Changed commit from 60505b0 to b9909c0

egourgoulhon · 2021-06-03T06:41:31Z

comment:39

I would not perform the import of ManifoldSubsetClosure in the EXAMPLES section, but rather construct the closure via the dedicated method closure(), since this is what the end user is supposed to do. In other words, I would rewrite the first part of the example as something like

sage: M = Manifold(2, 'R^2', structure='topological')
sage: c_cart.<x,y> = M.chart() # Cartesian coordinates on R^2
sage: D = M.open_subset('D', coord_def={c_cart: x^2+y^2<1}); D
Open subset D of the 2-dimensional topological manifold R^2
sage: cl_D = D.closure()
sage: cl_D
Topological closure cl_D of the Open subset D of the 2-dimensional
 topological manifold R^2
sage: latex(cl_D)
\mathop{\mathrm{cl}}(D)
sage: type(cl_D)
<class 'sage.manifolds.subsets.closure.ManifoldSubsetClosure_with_category'>
sage: cl_D.category()
Category of subobjects of sets

egourgoulhon · 2021-06-03T08:47:48Z

comment:40

Also, in the docstring of ManifoldSubset.closure(), it would be nice to add an OUTPUT field as follows:

OUTPUT:

- an instance of :class:`~sage.manifolds.subsets.closure.ManifoldSubsetClosure`

This allows one to easily access to the documentation of class ManifoldSubsetClosure from that of closure(). For completeness, one may also add an INPUT field describing the arguments name and latex_name and their default values.

sagetrac-git · 2021-06-03T18:04:26Z

Changed commit from b9909c0 to 16c6a72

sagetrac-git · 2021-06-03T18:04:26Z

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

`16c6a72`	`ManifoldSubsetClosure, ManifoldSubset.closure: Improve documentation`

mkoeppe · 2021-06-03T18:04:41Z

comment:42

Thanks for the suggestions, done.

egourgoulhon · 2021-06-03T22:20:36Z

Reviewer: Eric Gourgoulhon

egourgoulhon · 2021-06-03T22:20:36Z

comment:43

Thanks!

mkoeppe · 2021-06-03T23:16:50Z

comment:44

Thank you!

sagetrac-git · 2021-06-19T18:20:02Z

Changed commit from 16c6a72 to 9abc617

sagetrac-git · 2021-06-19T18:20:02Z

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

`359dde1`	`Merge branch 't/31727/manifoldsubset__add_methods_subset_family__superset_family__equal_subset_family__deprecate_method_list_of_subsets' into t/31732/manifoldsubset__new_methods_declare_empty__declare_nonempty__is_empty__has_defined_points__open_cover_family`
`fd4506a`	`Merge #31732`
`7fed9ef`	`Merge #31736`
`c4acd09`	`Merge tag '9.4.beta2' into t/31763/manifoldsubset__new_methods_declare_subset__declare_superset`
`2ba18ab`	`Merge #31763`
`0e9e5cd`	`Merge #31732`
`a96f736`	`Merge #31736`
`582b58d`	`Merge #31763`
`2113f78`	`Merge #31764`
`9abc617`	`Merge #31798`

mkoeppe · 2021-06-19T18:20:57Z

comment:46

Trivial merge of updated dependency #31763

vbraun · 2021-06-29T17:40:54Z

Changed branch from u/mkoeppe/topological_closure_of_embedded_submanifolds to 9abc617

mkoeppe added this to the sage-9.3 milestone Apr 10, 2021

mkoeppe added c: manifolds labels Apr 10, 2021

mkoeppe changed the title ~~Topological closure of embedded submanifolds~~ Topological closure of manifold subsets, embedded submanifolds Apr 11, 2021

mkoeppe modified the milestones: sage-9.3, sage-9.4 Apr 11, 2021

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egourgoulhon added s: positive review and removed s: needs review labels Jun 3, 2021

sagetrac-git mannequin added s: needs review and removed s: positive review labels Jun 19, 2021

mkoeppe added s: positive review and removed s: needs review labels Jun 19, 2021

vbraun removed the s: positive review label Jun 29, 2021

vbraun closed this as completed in b76884b Jun 29, 2021

egourgoulhon mentioned this issue Jan 30, 2023

SageManifolds metaticket 2 #30525

Open

This was referenced Jul 1, 2021

Connect RealSet to sage.manifolds #30832

Closed

Pullbacks (preimages) of manifold subsets under continuous maps #31688

Closed

Meta-ticket: Families, posets, complexes of manifold subsets #31740

Open

Topological closure of manifold subsets, methods ManifoldSubset.closure, is_closed, declare_closed #31644

Topological closure of manifold subsets, methods ManifoldSubset.closure, is_closed, declare_closed #31644

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mkoeppe commented Apr 10, 2021

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