#18529: Topological manifolds: basics
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: geometry | Resolution:
Keywords: topological | Merged in:
manifolds | Reviewers:
Authors: Eric Gourgoulhon | Work issues:
Report Upstream: N/A | Commit:
Branch: | 89c063c7119f19497e3d21b2a5a9dcb0752122b0
public/manifolds/top_manif_basics | Stopgaps:
Dependencies: #18175 |
-------------------------------------+-------------------------------------
Comment (by egourgoulhon):
Replying to [comment:2 jhpalmieri]:
> The phrase "manifold over a field K" sounds odd to me. Is it used in the
literature?
Thanks for your comment. You are right: this is an abusive generalization
of "manifold over R" and "manifold over C", which are used in the
literature.
>What if K is a finite field? It seems that if X is a finite discrete
space, for every finite field F and for every non-negative integer n, then
X is a manifold over F of dimension n: F and n play no role. (I'm assuming
that finite fields have been given the discrete topology.)
>
> I think you might say "topological manifold over a topological field K",
since obviously the topology on K is critical. Or you could omit "over a
field K", and mention in the documentation that users can specify a
topological field (like \CC, rather than the default \RR) if they want.
Thanks for your suggestion; I've modified the ticket description
accordingly. I've also added what is meant by "topological manifold over a
topological field K".
--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
