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Duality for generalized events. (English) Zbl 1076.22004

This paper extends to D-posets (resp. effect algebras) the author’s results he obtained for Boolean algebras and MV-algebras. He first introduces the category PB the objects of which are D-posets (= posets with an abstract set-difference) endowed with a convergence structure. He then shows as a main result that the category APB of absolute PB (i.e., those objects of PB which allow for unique morphism extensions provided they allow for extensions) is an epireflexive subcategory of PB. Finally, he finds a duality between PB and a category of D-posets related to measurability and sobriety.

MSC:

22A30 Other topological algebraic systems and their representations
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
60A05 Axioms; other general questions in probability
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