Connectedness Applied to Closure Spaces and State Property Systems

TL;DR

This paper explores the relationship between connectedness in closure spaces and classical properties in state property systems, providing a decomposition theorem that separates classical and nonclassical components.

Contribution

It introduces a decomposition theorem that splits a state property system into classical and nonclassical parts based on connectedness in closure spaces.

Findings

Decomposition of state property systems into classical and nonclassical parts

Connection between connectedness and classical properties in closure spaces

Theoretical framework for analyzing physical entities via closure spaces

Abstract

In earlier work a description of a physical entity is given by means of a state property system and it is proven that any state property system is equivalent to a closure space. In the present paper we investigate the relations between classical properties and connectedness for closure spaces. The main result is a decomposition theorem, which allows us to split a state property system into a number of 'pure nonclassical state property systems' and a 'totally classical state property system'