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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Profinite orthomodular lattices


Authors: Tae Ho Choe and Richard J. Greechie
Journal: Proc. Amer. Math. Soc. 118 (1993), 1053-1060
MSC: Primary 06C15; Secondary 06B30
MathSciNet review: 1143016
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Abstract: We prove that any compact topological orthomodular lattice $ L$ is zero dimensional. This leads one to show that $ L$ is profinite iff it is the product of finite orthomodular lattices with their discrete topologies. We construct a completion $ \overline L $ of a residually finite orthomodular lattice $ L$ having the property that every element of $ \overline L $ is the join of meets of elements of $ L$. Necessary and sufficient conditions for $ L$ that $ \overline L $ is the MacNeille completion are obtained.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1143016-9
PII: S 0002-9939(1993)1143016-9
Article copyright: © Copyright 1993 American Mathematical Society