Re: M Physics 21: Topology of seeing ~ Geometry of thinking

Posted by DickT on September 02, 2003 at 08:07:56:

In Reply to: M Physics 21: Topology of seeing ~ Geometry of thinking posted by kx21 on August 30, 2003 at 19:56:00:

kx21,

Please look at Klein's hierarchy of geometries, that sol discovered and posted on the M theory & duality board. Topology is the level of geometry where all you have is continuity. No lines, no angles, just convergent sequences and continuous functions.

It's amazing that any theorems at all could be proved with such meager resources, but the great topologists of the early 20th century met the challenge and built a rich theory of topological spaces.

In line with Klein's organization, every theorem that's true at the topological level(every theorem about pure continuity, that is) is true at the lower levels, projective, affine, and euclidean (the classical non-euclidean geometries fall at this level too).

Regards,
Dick

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