Uniform Theory of Geometric Spaces

TL;DR

This paper formalizes Yaglom's classification of geometric spaces into a universal, easy-to-use analytic framework that applies across all dimensions, serving as a foundation for the GeomSpace project.

Contribution

It introduces a formal, unified analytic theory of geometric spaces based on Yaglom's classification, expanding its applicability and usability.

Findings

Universal analytic framework for geometric spaces

Applicable across arbitrary dimensions

Supports the GeomSpace project

Abstract

Isaak Moiseevich Yaglom deduced complete classification of geometric spaces. In this work, supposed to your attention, author formalizes Yaglom's approach and constructs uniform theory of geometric spaces on analytic level. Among its advantages there are its universality and the fact it is easy to use. It isn't limited to specific dimension. The theory becomes the background of the GeomSpace project (http://sourceforge.net/projects/geomspace/).