#18529: Topological manifolds: basics
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-7.0
Component: geometry | Resolution:
Keywords: topological | Merged in:
manifolds | Reviewers: Travis Scrimshaw
Authors: Eric Gourgoulhon, | Work issues:
Travis Scrimshaw | Commit:
Report Upstream: N/A | 3cd03a48d847e12745ed8c25b23f19db141c179a
Branch: | Stopgaps:
public/manifolds/top_manif_basics |
Dependencies: #18175 |
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Comment (by egourgoulhon):
Giving a second thought to this, another hierarchy that would preserve the
distinction between whole manifolds and open subsets is
{{{
Hierarchy-3:
AbstractAmbient ManifoldSubset
| | | |
| | | OpenTopSubmanifold
| | \ / |
| | TopologicalManifold |
| | |
| | OpenDiffSubmanifold
| \ / |
| DifferentiableManifold |
| |
| OpenSubinterval
\____ ____/
OpenInterval
|
RealLine
}}}
The class `AbstractAmbient` would only implement the methods `union` and
`intersection`, which are trivial in this case. Each of the classes
`TopologicalManifold`, `DifferentiableManifold` and `OpenInterval` would
implement only the method `_repr_`.
Hierarchy-3 is simpler than Hierarchy-1 and does not require any mixin
class.
It is also easy to add a new structure, like complex manifolds.
Hierarchy-3 is also mathematically neat, since a topological (resp.
differentiable) manifold is obviously a open subset of a topological
(resp. differentiable) manifold. In this respect it reverses the logic of
Hierarchy-1, where the class `OpenTopSubmanifold` inherits from
`TopologicalManifold`, not the opposite. Maybe the latter logic is quite
well spread for ''algebraic'' structures in Sage, I mean classes for
substructures inheriting from classes for the ambient structure. But for
''topology'', the reverse logic, as proposed in Hierarchy-3, could be more
adapted: a topological space is often treated as an open subset of itself.
For instance, this occurs in its very definition: a topological space is a
set X endowed with a collection of subsets of X, called the open subsets,
such that the empty set and X are open, etc.
What do think?
--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:110>
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