#18175: Implement categories for topological and metric spaces and related
categories
-------------------------------------+-------------------------------------
       Reporter:  tscrim             |        Owner:  tscrim
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.10
      Component:  categories         |   Resolution:
       Keywords:  geometry,          |    Merged in:
  topology, sd67                     |    Reviewers:  Eric Gourgoulhon
        Authors:  Travis Scrimshaw   |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  f6fdd7ddad7fdbef37e7632d628f432891e76acc
  public/categories/topological_metric_spaces-18175|     Stopgaps:
   Dependencies:  #18174 #17160      |
-------------------------------------+-------------------------------------

Comment (by tscrim):

 Replying to [comment:61 egourgoulhon]:
 > I've merged the last commit of this ticket in all the tickets of #18528,
 replacing the `Sets()` category by `Manifolds(K)`,
 `Manifolds(K).Differentiable()` or `Manifolds(K).Smooth()`, with `K`=`RR`,
 `QQ`, `Qp(5)` or `CC`. Everything works well!

 That's very good to hear!

 > I've just one last question:
 >
 > In the examples (in `src/sage/categories/examples/manifolds.py` and
 `src/sage/categories/examples/cw_complexes.py`), the parents implement the
 method `an_element` and not `_an_element_` (as advised in the Parent
 section of the reference manual). Is there any reason for this?

 The reason we have `_an_element_` was for caching before there was an
 `@cached_method`. It is sufficient to implement `an_element`, especially
 for example classes. However, I can change if it you feel I should.

 > and three suggestions of typo corrections

 All done (and some other pyflakes cleanup).

--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:63>
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