A Logical Reading of the Nonexistence of Proper Homomorphisms between Affine Spaces

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)215-218
Number of pages4
JournalGeometriae Dedicata
Volume81
Issue number1-3
DOIs
StatePublished - Jan 1 2000

Keywords

  • Affine geometry
  • Definability
  • Lyndon's preservation theorem

ASJC Scopus subject areas

  • Geometry and Topology

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