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Connectedness applied to closure spaces and state property systems

Summary: Connectedness applied to closure spaces and
state property systems
D. Aerts, D. Deses, A. Van der Voorde
Department of Mathematics, Brussels Free University,
Pleinlaan 2, B-1050 Brussels, Belgium
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


Source: Aerts, Diederik - Leo Apostel Centre, Vrije Universiteit Brussel


Collections: Multidisciplinary Databases and Resources; Physics