# Operational approach to the topological structure of the physical space

## TL;DR

This paper presents an operational method to reconstruct geometric and topological features of physical space from basic assumptions, defining fundamental concepts within a formalism closely connected to nature.

## Contribution

It introduces a novel axiomatic approach that defines points, lines, and planes operationally, differing from traditional axiomatic systems by grounding concepts in natural assumptions.

## Key findings

- Primitive concepts are defined within the formalism.
- The approach connects axioms closely with physical nature.
- Potential pedagogical benefits are discussed.

## Abstract

Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and topology in a fully operational manner. Curiously enough, primitive concepts such as points, spaces, straight lines, planes are all defined within our formalism. Our construction breaks down with the usual literature, as our axioms have deep connection with nature. Besides that, we hope this operational approach could also be of pedagogical interest.