International Journal of Theoretical Physics

, Volume 44, Issue 12, pp 2283–2293 | Cite as

The Canonical Topology on a Meet-Semilattice

  • Isar Stubbe


Considering the lattice of properties of a physical system, it has been argued elsewhere that—to build a calculus of propositions having a well-behaved notion of disjunction (and implication)—one should consider a very particular frame completion of this lattice. We show that the pertinent frame completion is obtained as sheafification of the presheaves on the given meet-semilattice with respect to its canonical Grothendieck topology, an explicit description of which is easily given. Our conclusion is that there is an intrinsic categorical quality to the notion of “disjunction” in the context of property lattices of physical systems.


meet-semilattice topology sheaf frame completion 


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© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Département de MathématiqueUniversité de LouvainLouvain-la-NeuveBelgium

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