Homogeneous and ultrahomogeneous linear spaces

摘要

A linear space S is homogeneous if, whenever the linear structures induced on two finite subsets S' and S " are isomorphic, there is at least one automorphism of S mapping S' onto S ". If every isomorphism from S' to S " can be extended to an automorphism of S, S is called ultrahomogeneous. We give a complete classification of all homogeneous (resp. ultrahomogeneous) linear spaces, without making any finiteness assumption on the number of points of S. (C) 1998 Academic Press. [References: 10]