| | |
Summary: State property systems and closure spaces:
a study of categorical equivalence
Diederik Aerts, Eva Colebunders, Ann Van der Voorde and
Bart Van Steirteghem
FUND and TOPO,
Department of Mathematics, Brussels Free University,
Pleinlaan 2, B-1050 Brussels, Belgium
CLEA,
Brussels Free University,
Krijgskundestraat 33, 1160 Brussels, Belgium
e-mails: diraerts@vub.ac.be, evacoleb@vub.ac.be,
avdvoord@vub.ac.be, bvsteirt@vub.ac.be
Abstract
We show that the natural mathematical structure to describe a physical
entity by means of its states and its properties within the Geneva-Brussels
approach is that of a state property system. We prove that the category of
state property systems (and morphisms), SP, is equivalent to the category
of closure spaces (and continuous maps), Cls. We show the equivalence
of the `state determination axiom' for state property systems with the `T0
separation axiom' for closure spaces. We also prove that the category SP0
|
