Order-topological separable complete modular ortholattices admit order continuous faithful valuations
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Abstract:
We prove that on every separable complete atomic modular ortholattice (i.e. order topological) there exists an order continuous faithful valuation. We also give a construction of the existing order continuous faithful valuation. For separable atomic modular ortholattices we give a necessary and sufficient condition to admit an order continuous faithful valuation and we show that it is equivalent with the condition to have a modular MacNeille completion. We improve one statement on complete metric lattices from Birkhoff’s Lattice Theory.References
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Additional Information
- Zdenka Riečanová
- Affiliation: Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak Technical University, Ilkovičova 3, 812 19 Bratislava, Slovak Republic
- Email: zriecan@elf.stuba.sk
- Received by editor(s): March 12, 1996
- Received by editor(s) in revised form: June 26, 1996
- Communicated by: Lance W. Small
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 231-237
- MSC (1991): Primary 03G12, 06C15, 06F30
- DOI: https://doi.org/10.1090/S0002-9939-98-04072-6
- MathSciNet review: 1415337