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.
@article{bwmeta1.element.bwnjournal-article-cmv62i1p7bwm,
author = {Josef Tkadlec},
title = {Partially additive states on orthomodular posets},
journal = {Colloquium Mathematicae},
volume = {62},
year = {1991},
pages = {7-14},
zbl = {0784.03037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv62i1p7bwm}
}
Tkadlec, Josef. Partially additive states on orthomodular posets. Colloquium Mathematicae, Tome 62 (1991) pp. 7-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv62i1p7bwm/
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