Download or read book Collinearity-Preserving Functions between Desarguesian Planes written by David S. Carter and published by American Mathematical Soc.. This book was released on 1980 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using concepts from valuation theory, we obtain a characterization of all collinearity-preserving functions from one affine or projective Desarguesian plane into another. The case in which the planes are projective and the range contains a quadrangle has been treated previously in the literature. Our results permit one or both planes to be affine and include cases where the range contains a triangle but no quadrangle. A key theorem is that, with the exception of certain embeddings defined on planes of order 2 and 3, every collinearity-preserving function from one affine Desarguesian plane into another can be extended to a collinearity-preserving function between enveloping projective planes.