#18175: Implement categories for topological and metric spaces and related
categories
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.6
Component: categories | Resolution:
Keywords: geometry, | Merged in:
topology, sd67 | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | fcc3273fbb9e83da6c61027463e3ed4582009514
public/categories/topological_metric_spaces-18175| Stopgaps:
Dependencies: #18174 #17160 |
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Comment (by tscrim):
Replying to [comment:9 egourgoulhon]:
> Replying to [comment:8 tscrim]:
> > I wasn't sure about the dimension making sense for manifolds unless
they are connected as far as my definition. Mainly do we want the disjoint
union of a 1-sphere and 2-sphere be a manifold? (Current definition is
yes). If so, then is the dimension the maximal dimension of each
component? I will leave the decision up to you.
>
> For all the textbook definitions I am aware of, the disjoint union of a
1-sphere and a 2-sphere is *not* a manifold. In other words, the dimension
is unique among all the connected components of the manifold. So I think
the dimension should be at the level of `Manifolds`.
I split the difference in that I kept a more general definition, but I had
dimension be the maximum of the dimensions of each connected component so
you don't necessarily have to specify connected.
> > > - in the docstring of `Manifolds`, I think the phrase "such that the
neighborhood of any point `x \in M` is homeomorphic to `k^d`" should be
changed to something like "such that any point `x\in M` admits a
neighborhood homeomorphic to `k^d`"
> >
> > Feel free to change the docstrings and categories as much as you want.
However if you just want to get these category stubs into Sage as a
smaller step, we can do that too.
>
> Apart from the dimension issue discussed above, the current categories
seems fine to rebase !SageManifolds on them, thanks. I'll try soon and let
you know.
I made some fixes, specifically I stopped an infinite recursion with
metric spaces caused by some of my last-minute refactoring. I forgot to
make the other change to the manifold's doc, but I want to make sure
you're okay with my definition of a manifold before I keep changing it.
This is almost ready for review up to some methods not containing
doctests.
--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:11>
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