|Author||: David S. Carter|
|File Size||: 42,5 Mb|
|Publisher||: American Mathematical Soc.|
|Release Date||: 29 September 1980|
|Pages||: 98 pages|
Collinearity Preserving Functions between Desarguesian Planes by David S. Carter Book PDF Summary
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.