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

Riečanová, Zdenka

doi:10.1090/S0002-9939-98-04072-6

Order-topological separable complete modular ortholattices admit order continuous faithful valuations
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Proc. Amer. Math. Soc. 126 (1998), 231-237 Request permission

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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