Axioms of Heterogeneous Geometry

This study is based on Lobachevsky’s hypothesis that different parts of space satisfy different geometries such as the Euclidean, non-Euclidean, and projective ones. Based on the theory of arithmetic graphs, three systems of algebraic equations were constructed that are embedded in a discrete metric space in which a point is an integer allowing to define a straight line, a plane, and other elements except for 0.