Parallelity Spaces 1

Summary. In the monography [5] W. Szmielew introduced the parallelity planes 〈S; �〉, where � ⊆ S×S×S×S. In this text we omit upper bound axiom which must be satisfied by the parallelity planes (see also E.Kusak [3]). Further we will list those theorems which remain true when we pass from the parallelity planes to the parallelity spaces. We construct a model of the parallelity space in Abelian group 〈F ×F ×F;+F, −F,0F 〉, where F is a field. MML Identifier: PARSP 1. The papers [7], [6], [2], [1], and [4] provide the terminology and notation for thi