Mathematical methods in region-based theories of space: the case of Whitehead points

TL;DR

This paper explores how mathematical tools can validate Whitehead's region-based approach to defining points, demonstrating that these objects serve as fundamental components of certain topological spaces.

Contribution

It provides a mathematical framework to confirm that Whitehead's region-based objects are indeed points in a topological space, advancing the understanding of space construction.

Findings

Whitehead's method constructs objects that are points in topological spaces

Mathematical tools can verify the point-like nature of Whitehead's objects

The approach bridges regions-based theories with classical topology

Abstract

Regions-based theories of space aim -- among others -- to define points in a geometrically appealing way. The most famous definition of this kind is probably due to Whitehead. However, to conclude that the objects defined are points indeed, one should show that they are points of a geometrical or a topological space constructed in a specific way. This paper intends to show how the development of mathematical tools allows showing that Whitehead's method of extensive abstraction provides a construction of objects that are fundamental building blocks of specific topological spaces.