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

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

Closed mkoeppe closed 3 years ago

mkoeppe commented 3 years ago

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

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

16c6a72 ManifoldSubsetClosure, ManifoldSubset.closure: Improve documentation

mkoeppe commented 3 years ago

comment:42

Thanks for the suggestions, done.

egourgoulhon commented 3 years ago

Reviewer: Eric Gourgoulhon

egourgoulhon commented 3 years ago

comment:43

Thanks!

mkoeppe commented 3 years ago

comment:44

Thank you!

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 16c6a72 to 9abc617

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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 commented 3 years ago

comment:46

Trivial merge of updated dependency #31763

vbraun commented 3 years ago

Changed branch from u/mkoeppe/topological_closure_of_embedded_submanifolds to 9abc617