Quantized spaces are four-dimensional compact manifolds with de-Sitter (O(1,4) or O(2,3)) group of motion

Abstract

It is shown uniquely that quantized spaces are realised on four-dimensional compact manifolds. In the case of O(1,5) quantized space this are four independent parameters of O(5) unit vector; in the case of O(2,4) these are parameters of one two-dimensional unit vector (1 parameter) and components of unit four-dimensional vector (3- parameters) and at last in the case O(3,3) these are parameters of 2 independent 3-dimensional unit vectors (each have 2 parameters). This result follows directly only from the condition to have a correct limit to usual theory (correspondence principle).