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Proceedings of the American Mathematical Society

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Order-topological separable complete
modular ortholattices admit order
continuous faithful valuations

Author: Zdenka Riecanová
Journal: Proc. Amer. Math. Soc. 126 (1998), 231-237
MSC (1991): Primary 03G12, 06C15, 06F30
MathSciNet review: 1415337
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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.

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Additional Information

Zdenka Riecanová
Affiliation: Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak Technical University, Ilkovičova 3, 812 19 Bratislava, Slovak Republic

Keywords: Order convergence, order topology, order-topological, modular ortholattice, valuation, strongly compactly atomistic, MacNeille completion
Received by editor(s): March 12, 1996
Received by editor(s) in revised form: June 26, 1996
Communicated by: Lance W. Small
Article copyright: © Copyright 1998 American Mathematical Society