We provide definitions of ≠ and of noncollinearity by positive statements in terms of the ternary predicate of collinearity which are valid in affine n-dimensional geometry. This provides the intrinsic reason for the validity of V. Corbas's theorem stating that surjective maps between affine planes that preserve collinearity are isomorphisms, and of P. Maroscia's higher-dimensional generalization thereof.
- Affine geometry
- Lyndon's preservation theorem
ASJC Scopus subject areas
- Geometry and Topology