Homogeneous and Ultrahomogeneous Linear Spaces

A linear spaceSishomogeneousif, whenever the linear structures induced on two finite subsetsS′ andS″ are isomorphic, there is at least one automorphism ofSmappingS′ ontoS″. If every isomorphism fromS′ toS″ can be extended to an automorphism ofS,Sis calledultrahomogeneous. We give a complete classification of all homogeneous (resp. ultrahomogeneous) linear spaces, without making any finiteness assumption on the number of points ofS.