#18175: Implement categories for topological and metric spaces and related
categories
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: categories | Resolution:
Keywords: geometry, | Merged in:
topology, sd67 | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | e6076d2a41dbe5e3294c03a95e3e763e60d554ff
public/categories/topological_metric_spaces-18175| Stopgaps:
Dependencies: #18174 #17160 |
-------------------------------------+-------------------------------------
Comment (by egourgoulhon):
Hi Travis,
Replying to [comment:33 tscrim]:
> Given our discussion, I have reorganized the manifolds category as:
> {{{
> Manifolds
> / \
> Complex Real
> |
> Differentiable
> |
> Smooth
> / \
> Analytic AlmostComplex
> }}}
It seems to me that `Real` should not be atop `Differentiable` in this
hierarchy. Indeed, there exist differentiable manifolds over fields other
than '''R''' or '''C''': for instance differentiable manifolds over the
field of p-adic numbers, '''Q'''_p: see e.g. Part II of J.-P. Serre's book
''Lie Algebras and Lie Groups'' (1992), where differentiable (actually
analytic) manifolds over '''Q'''_p are introduced. For this reason, in the
refactoring of !SageManifolds I am preparing in #18783, I have left the
base field generic (notice that we do have the fields of p-adic numbers in
Sage). So it would be nice to be able to set the category to
`Manifolds().Differentiable()` without having to assume that the base
field is '''R'''. Similarly, I think that `Complex` should be a
subcategory of `Analytic`. As you suggest in comment:35, maybe `Complex`
and `Real` should be axioms, rather than appearing in the above
hierarchy...
> I've added full doctest coverage and some examples. So ready for proper
review.
>
> PS - Sorry it took so long to get back to this.
Thank you for working on this!
--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:36>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
