Isomorphisms of linear spaces

Related pages

Isomorphisms of projective planes
80 We may think of isomorphisms between partial linear spaces as special bijections between their sets of points. If both partial linear spaces are in fact linear spaces, then the criterion to check for an isomorphism can be simplified. The following simple lemma holds.

Lemma. Given two linear spaces and , then a bijection is an isomorphism of linear spaces if and only if for each line l of .

Hence, it's enough to check that each line is mapped onto another line.

Contributed by Hauke Klein
Version $Id: liniso.html,v 1.2 2001/01/01 18:07:34 hauke Exp $