#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: | aea3a7dea7fb5325b4e950be6c4c76b64c491cdd
public/categories/topological_metric_spaces-18175| Stopgaps:
Dependencies: #18174 #17160 |
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Comment (by egourgoulhon):
Replying to [comment:8 tscrim]:
> Replying to [comment:7 egourgoulhon]:
> > - the methods `dimension()` and `FiniteDimensional()`, and well as the
class `FiniteDimensional`, are defined only at the level of `Connected`;
shouldn't they be at the level of `Manifolds` itself ?
>
> 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`.
>
> > - 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.
--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:9>
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