#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-6.8
Component: categories | Resolution:
Keywords: geometry, | Merged in:
topology, sd67 | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 5796cbd4fd66bdad4df405a4942f47e9d9d9c69a
public/categories/topological_metric_spaces-18175| Stopgaps:
Dependencies: #18174 #17160 |
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Comment (by egourgoulhon):
Replying to [comment:14 tscrim]:
> On Wikipedia (http://en.wikipedia.org/wiki/Dimension), they are careful
to say a connected manifold.
Yes. I've looked a little further and found that some authors do allow for
different dimensions on different connected components; they then define a
''pure manifold'' as a manifold for which the dimension is the same among
all connected components. On the other side, other authors refuse to do
this: for instance, J.M. Lee, in his Introduction to Topological Manifolds
(2nd ed., 2011) says on p. 39: ''"the first remark is that the definition
of a manifold requires that every manifold have a specific, well-defined
dimension. This rules out, for example, spaces such as a disjoint union of
a line and a plane in R^3^ ".''
Since there is no consensus in the literature, it's fine to take either
definition, as long as it is clearly stated. I therefore agree with your
definition, especially since it is consistent with CW complexes.
--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:15>
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