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

Research output: Contribution to journalArticle

3 Citations (Scopus)

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
StatePublished - 2000

Fingerprint

Collinearity
Affine Space
Homomorphisms
Nonexistence
Affine plane
Ternary
Predicate
n-dimensional
Isomorphism
High-dimensional
Valid
Theorem
Generalization

Keywords

  • Affine geometry
  • Definability
  • Lyndon's preservation theorem

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

A Logical Reading of the Nonexistence of Proper Homomorphisms between Affine Spaces. / Pambuccian, Victor.

In: Geometriae Dedicata, Vol. 81, No. 1-3, 2000, p. 215-218.

Research output: Contribution to journalArticle

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