Topology

Topology (by Poincaré)

Moniker “Rubber-Sheet Geometry“, compared with Geometry’s ‘rigid objects‘.

[Greek]= τοΠοζ(Place) λΟγια(Study)
[Latin]= Analysis Situs (Situation)

1. Remove (invariants) of geometry:

  • a. Euclidean (distance)
  • b. Affine (//, ratio)
  • c. Projective (cross-ratio)

2. Preserve ‘Neighbourhood’ (Nearness)

  • define ‘Continuity’ (Analysis)

3. Elastic deformation (stretch, bend, twist)

  • a line is no longer a line.

 

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