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.
Mathtuition88 