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Title

Partially additive states on orthomodular posets

Authors 1

Affiliations

  1. Department of Mathematics, Faculty of Electrical Engineering, Technical University of Prague, 166 27 Praha, Czechoslovakia

Abstract

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.

Bibliography

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Colloquium Mathematicum
1991/62/1
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Pages:
7-14
Main language of publication
English
Received
1989-01-16
Accepted
1989-05-15
Published
1991
Exact and natural sciences