Opened 4 years ago
Last modified 3 years ago
#18529 closed enhancement
Topological manifolds: basics — at Version 3
Reported by: | egourgoulhon | Owned by: | egourgoulhon |
---|---|---|---|
Priority: | major | Milestone: | sage-7.1 |
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: | 89c063c7119f19497e3d21b2a5a9dcb0752122b0 |
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 meta-ticket #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 non-negative 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 manifoldTopManifoldOpenSubset
: open subset of a topological manifold
Chart
: 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 (3)
comment:1 Changed 4 years ago by
- Description modified (diff)
comment:2 Changed 4 years ago by
comment:3 Changed 4 years ago by
- Description modified (diff)
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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 non-negative 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.