A topology on quantum logics
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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Keywords: Orthomodular lattice, quantum logic, uniform topology generated by measures
Article copyright: © Copyright 1989 American Mathematical Society