#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 tscrim):
I don't really hold a strong opinion on the definition of a manifold, so
perhaps for the sake of clarity, we'll make this be local homeomorphic to
'''k'''^n^, where '''k''' is a topological field.
However this brings up another point in the design for manifolds. When I
first wrote this category, I was thinking all manifolds would be real and
a subcategory for those who allow carry a complex structure. The reason
for this is I was thinking of complex Lie groups, which can behave
differently than their real/rational/positive-char counterparts. Yet I'm
wondering if we should instead just parameterize the category and this
gives a more consistent interface (and if we need a special complex
subcategory, we still might want that parameterized by the complex field).
A more concrete (better) question is what do you want a complex manifold
to be? Wikipedia says it is a manifold with holomorphic transition maps.
Or should this be a smooth manifold over the complex numbers? In other
words, should the notion of differentiability be inherent in the base
field?
Thoughts?
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Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:17>
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