#18529: Topological manifolds: basics
-------------------------------------+-------------------------------------
       Reporter:  egourgoulhon       |        Owner:  egourgoulhon
           Type:  enhancement        |       Status:  needs_info
       Priority:  major              |    Milestone:  sage-7.0
      Component:  geometry           |   Resolution:
       Keywords:  topological        |    Merged in:
  manifolds                          |    Reviewers:  Travis Scrimshaw
        Authors:  Eric Gourgoulhon,  |  Work issues:
  Travis Scrimshaw                   |       Commit:
Report Upstream:  N/A                |  c38ae80cbd8032cf7041259284b6f646265d1e42
         Branch:                     |     Stopgaps:
  public/manifolds/top_manif_basics  |
   Dependencies:  #18175             |
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Comment (by tscrim):

 Then how about we have a `_distinguished_open_cover`, which is set to the
 first open cover that gets added? IMO, this will be

 - lightweight (just a pointer);
 - (marginally) faster (only an attribute lookup instead of attribute plus
 index grab; granted, this speedup will probably never be noticable);
 - keep the `O(1)` checking speed of something being an open cover;
 - and more robust when doing the comparisons (we check to see if the
 distinguished open cover is an open cover of the other one, so we don't
 have to worry about things breaking if something ends up being out of
 order in the creating of the open cover list).

 It means one additional attribute we'll have to manage, but I think that
 is an epsilon cost.

--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:99>
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