#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: | 95a30aa57fc62f23a884790b57835d107d8bdeef
public/categories/topological_metric_spaces-18175| Stopgaps:
Dependencies: #18174 #17160 |
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Comment (by egourgoulhon):
Hi Basile,
Replying to [comment:29 bpillet]:
>
>
> As I said, there are case for some fields '''K''' where '''K'''-analytic
is weaker than expected : For example I can make a change of charts x -->
x^p^ over F_p which is actually invertible since x^p^ is the identity on
F_p but when computing its differential it vanishes identically since
px^p-1^ = 0 in caracteristic p.
Thanks for this example!
> In my opinion (which is strongly disputable as I don't have a very wide
knowledge of the existing theories) differential geometry is meant for
'''R''' and '''C''' (or maybe in extremal cases over p-adic fields) but
over other field the right way of doing geometry is through algebraic
geometry : Manifolds or varieties are no longer given by charts but by
equations.
Yes, you are right, for differentiable manifolds, we should probably limit
ourselves to '''K'''='''C''' or '''K'''='''R''' (at least in a first
stage). In the refactoring of !SageManifolds I am preparing for #18528, I
leave the base field generic anyway. In the documentation of class
`TopManifold` in #18529, you can see already an example with
'''K'''='''C''' (the Riemann sphere as a topological manifold of dimension
1 over '''C''').
--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:30>
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