#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 egourgoulhon):
Replying to [comment:11 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.
Do you have a reference for such a definition of a manifold ? It seems
non-standard (*) to me, but I might be wrong.
(*) the standard being that the dimension is the same for all the
connected components.
--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:12>
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