Opened 6 years ago
Last modified 6 years ago
#18529 closed enhancement
Topological manifolds: basics — at Version 9
Reported by:  egourgoulhon  Owned by:  egourgoulhon 

Priority:  major  Milestone:  sage7.1 
Component:  geometry  Keywords:  topological manifolds 
Cc:  mmancini  Merged in:  
Authors:  Eric Gourgoulhon  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  public/manifolds/top_manif_basics  Commit:  fb96562c1e7d4ffc76ca87efcc15d133c6c15190 
Dependencies:  #18175  Stopgaps: 
Description (last modified by )
This is the implementation of topological manifolds over a topological field K resulting from the SageManifolds project. See the metaticket #18528 for an overview. By topological manifold over a topological field K it is meant a second countable Hausdorff space M such that every point in M has a neighborhood homeomorphic to K^{n}, with the same nonnegative integer n for all points.
This tickets implements the following Python classes:
TopManifold
: topological manifold over a topological field KTopManifoldPoint
: point in a topological manifoldTopManifoldSubset
: generic subset of a topological manifoldChart
: chart of a topological manifoldRealChart
: chart of a topological manifold over the real field
CoordChange
: transition map between two charts of a topological manifold
TopManifold
is intended to serve as a base class for specific manifolds, like smooth manifolds (K=R) and complex manifolds (K=C).
Change History (9)
comment:1 Changed 6 years ago by
 Description modified (diff)
comment:2 followup: ↓ 4 Changed 6 years ago by
comment:3 Changed 6 years ago by
 Description modified (diff)
comment:4 in reply to: ↑ 2 Changed 6 years ago by
Replying to jhpalmieri:
The phrase "manifold over a field K" sounds odd to me. Is it used in the literature?
Thanks for your comment. You are right: this is an abusive generalization of "manifold over R" and "manifold over C", which are used in the literature.
What if K is a finite field? It seems that if X is a finite discrete space, for every finite field F and for every nonnegative integer n, then X is a manifold over F of dimension n: F and n play no role. (I'm assuming that finite fields have been given the discrete topology.)
I think you might say "topological manifold over a topological field K", since obviously the topology on K is critical. Or you could omit "over a field K", and mention in the documentation that users can specify a topological field (like \CC, rather than the default \RR) if they want.
Thanks for your suggestion; I've modified the ticket description accordingly. I've also added what is meant by "topological manifold over a topological field K".
PS: note that the code in the associated branch is still in a very crude draft state, but should be ready for review within a few days.
comment:5 Changed 6 years ago by
 Commit changed from 89c063c7119f19497e3d21b2a5a9dcb0752122b0 to 5a5722b4a0ef33d8624fdd127bbb1964232ced96
Branch pushed to git repo; I updated commit sha1. New commits:
5a5722b  Add doctests in classes Chart and RealChart

comment:6 Changed 6 years ago by
 Commit changed from 5a5722b4a0ef33d8624fdd127bbb1964232ced96 to 4f490af5fedeb0a28dd8ddab70efdab1cc64bf93
Branch pushed to git repo; I updated commit sha1. New commits:
4f490af  Improve the documentation of coordinate charts

comment:7 Changed 6 years ago by
 Commit changed from 4f490af5fedeb0a28dd8ddab70efdab1cc64bf93 to d8df59f286da79e1e103b56064fdffb702e034ce
Branch pushed to git repo; I updated commit sha1. New commits:
d8df59f  Improve the documentation of TopManifold

comment:8 Changed 6 years ago by
 Commit changed from d8df59f286da79e1e103b56064fdffb702e034ce to fb96562c1e7d4ffc76ca87efcc15d133c6c15190
Branch pushed to git repo; I updated commit sha1. New commits:
fb96562  Open subsets of topological manifolds are now fully considered as topological manifolds.

comment:9 Changed 6 years ago by
 Description modified (diff)
The phrase "manifold over a field K" sounds odd to me. Is it used in the literature? What if K is a finite field? It seems that if X is a finite discrete space, for every finite field F and for every nonnegative integer n, then X is a manifold over F of dimension n: F and n play no role. (I'm assuming that finite fields have been given the discrete topology.)
I think you might say "topological manifold over a topological field K", since obviously the topology on K is critical. Or you could omit "over a field K", and mention in the documentation that users can specify a topological field (like \CC, rather than the default \RR) if they want.