Questions of size...

[Sampo A Syreeni]

On Mon, 11 Dec 2000, R. A. Hettinga wrote:

>> Chambers defines geodesic as "the shortest line on a surface between two
>> points on it"
>
>Thank you. It works in all dimensions, and, thus it's topological, right?

Topology does not deal with dimension or distance. Pure geometry. Not even
affine or anything. As I've seen them defined, geodesics do not necessarily
mean the shortest path but rather the shortest path based on local
knowledge. I.e. if you have a wormhole in general relativity, the possible
shortcut does not affect the definition of geodesics in any way. You
calculate the geodesic based on the local curvature measure of the space,
that's it.

Sampo Syreeni <decoy at iki.fi>, aka decoy, student/math/Helsinki university