Geodesic
Partially additive states on orthomodular posets
Colloquium Mathematicum, Tome 62 (1991) no. 1, pp. 7-14.

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We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s:P → [0,1] which respect the ordering and the orthocomplementation in P and which are additive on B. We call such functions B-states on P. We first show that every P possesses "enough" two-valued B-states. This improves the main result in [13], where B is the centre of P. Moreover, it allows us to construct a closure-space representation of orthomodular lattices. We do this in the third section. This result may also be viewed as a generalization of [6]. Then we prove an extension theorem for B-states giving, as a by-product, a topological proof of a classical Boolean result.
DOI : 10.4064/cm-62-1-7-14

Josef Tkadlec 1

1 
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Josef Tkadlec. Partially additive states on orthomodular posets. Colloquium Mathematicum, Tome 62 (1991) no. 1, pp. 7-14. doi : 10.4064/cm-62-1-7-14. http://geodesic.mathdoc.fr/articles/10.4064/cm-62-1-7-14/

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