A topology on quantum logics

Authors:
Sylvia Pulmannová and Zdena Riečanová

Journal:
Proc. Amer. Math. Soc. **106** (1989), 891-897

MSC:
Primary 81B10; Secondary 06C15, 54A99

DOI:
https://doi.org/10.1090/S0002-9939-1989-0967488-4

MathSciNet review:
967488

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Abstract: A uniform topology induced by a set of finite measures on a quantum logic is studied. If is a valuation on , the topology induced by is equivalent to the topology induced by the pseudometric . If the set of measures is large enough, the topology reflects in some sense the structure of : if is a continuous geometry and the measures are totally additive, is weaker than the order topology on . If is atomic, is stronger than . On a separable Hilbert space logic, coincides with the discrete topology. Some cases are found in which .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0967488-4

Keywords:
Orthomodular lattice,
quantum logic,
uniform topology generated by measures

Article copyright:
© Copyright 1989
American Mathematical Society