#18175: Implement categories for topological and metric spaces and related
categories
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
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: | e6076d2a41dbe5e3294c03a95e3e763e60d554ff
public/categories/topological_metric_spaces-18175| Stopgaps:
Dependencies: #18174 #17160 |
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Comment (by egourgoulhon):
Replying to [comment:40 tscrim]:
> Just to make sure, so should we only allow complete metric fields as
input for differentiable manifolds? The alternative seems to be we allow
more general topological fields with perhaps some machinery to make
analytic manifolds over finite fields be non-smooth. Let me know what you
think is best.
I would favor the second alternative, i.e. not to restrict to complete
metric fields. In particular, there are some attempts to define
differentiable manifolds over general topological fields, see e.g.
[http://arxiv.org/abs/math/0502168 math/0502168]. Basile, John, Nicolas,
do you agree ?
PS: even if we don't demand that the base fields for differentiable
manifolds are complete metric spaces, it would be nice to have an axiom
"complete" for the category of metric spaces, as you suggest in
comment:39.
--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:41>
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