State property systems and closure spaces: a study of categorical equivalence

Simple item page
dc.creatorAerts, Diederik
dc.creatorColebunders, Eva
dc.creatorVan der Voorde, Ann
dc.creatorVan Steirteghem, Bart
dc.date2001-05-23
dc.date.accessioned2026-07-07T06:02:07Z
dc.date.available2026-07-07T06:02:07Z
dc.descriptionWe 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 of state determined state property systems is equivalent to the category L0 of based complete lattices. In this sense the equivalence of SP and Cls generalizes the equivalence of Cls0 and L0, proven in Erne 1984.
dc.description27 pages, 0 figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0105108
dc.identifierhttp://arxiv.org/abs/quant-ph/0105108
dc.identifierInternational Journal of Theoretical Physics, 38, 1999, 259
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/89497
dc.subjectQuantum Physics
dc.titleState property systems and closure spaces: a study of categorical equivalence
dc.typetext

Files

Collections

arXiv