 
Summary: Connectedness applied to closure spaces and
state property systems
D. Aerts, D. Deses, A. Van der Voorde
FUND and TOPO,
Department of Mathematics, Brussels Free University,
Pleinlaan 2, B1050 Brussels, Belgium
diraerts,diddesen,avdvoord@vub.ac.be
Abstract
In [1] a description of a physical entity is given by means of a state
property system and in [2] 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'.
1 Introduction
In [1] a physical entity is represented by a mathematical model called a state
property system. This model contains a complete lattice of properties of the
physical entity. In [2] it is shown that the lattice can viewed as the lattice of
closed sets of a closure space. We introduce the concept of classical property
