[FoRK] Succinct Trig
James Tauber <
jtauber at jtauber.com
> on >
Wed Jul 5 20:25:45 PDT 2006
>> And it's hardly a *topological* generalization. Topological
>> generalizations ignore notions like that of a normal.
> In the topology of manifolds, you have vectors that
> are normal to generalized surfaces.
Only if you define a metric on the manifold. Manifolds in general
need not have a notion of normals. And even manifolds are richer than
mere topological spaces, so the notion of a manifold (much less an
inner product) disappears under topological generalization.
The only concepts that survive topological generalization are
topological properties (i.e. those that are only based on the choice
of open sets) such as connectedness, compactness, etc.
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