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18529 Topological manifolds: basics egourgoulhon egourgoulhon "This is the implementation of topological manifolds over a topological field ''K'' resulting from the [http://sagemanifolds.obspm.fr/ 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:
- `ManifoldSubset`: generic subset of a topological manifold (the open subsets being implemented by the subsclass `TopologicalManifold`)
- `TopologicalManifold`: topological manifold over a topological field ''K''
- `ManifoldPoint`: point in a topological manifold
- `Chart`: chart of a topological manifold
- `RealChart`: chart of a topological manifold over the real field
- `CoordChange`: transition map between two charts of a topological manifold
as well as the singleton classes`TopologicalStructure` and `RealTopologicalStructure`.
`TopologicalManifold` is intended to serve as a base class for specific manifolds, like smooth manifolds (''K''='''R''') and complex manifolds (''K''='''C'''). The follow-up ticket, implementing continuous functions to the base field, is #18640.
'''Documentation''':
The reference manual is produced by
`sage -docbuild reference/manifolds html`
It can also be accessed online at http://sagemanifolds.obspm.fr/doc/18529/reference/manifolds/
More documentation (e.g. example worksheets) can be found [http://sagemanifolds.obspm.fr/documentation.html here].
" enhancement closed major sage-7.1 geometry fixed topological manifolds mmancini Eric Gourgoulhon, Travis Scrimshaw Travis Scrimshaw, Eric Gourgoulhon N/A 00d265cf2855121dba914868264da6ea3a9c42af 00d265cf2855121dba914868264da6ea3a9c42af #18175