A characterization of some partial geometric spaces (Q1065388)

A partial geometric space S of dimension \(m\geq 2\) consists of the sets \((A_ i)^{i=m}_{i=-1}\) and the set T, the elements of which are called flags. The authors enumerate the eight axioms to be satisfied by \(A_ i\) and T. There is a relation (called incidence) between the elements of \(A_ i\) based on the flags. Two examples are given of which the second is the finite projective geometry PG(m,q). The main part of the paper deals with an ingenious proof (split up into no less than eleven lemma's) for a property of S if it satisfies certain conditions. Another example of a partial geometric space (of dimension \(m\geq 3)\) is added.