Profinite orthomodular lattices
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- by Tae Ho Choe and Richard J. Greechie PDF
- Proc. Amer. Math. Soc. 118 (1993), 1053-1060 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 1053-1060
- MSC: Primary 06C15; Secondary 06B30
- DOI: https://doi.org/10.1090/S0002-9939-1993-1143016-9
- MathSciNet review: 1143016