Topologies on quantum logics induced by measures. (English) Zbl 0674.03021

The author discusses, from the topological point view, the compatibility of two or more elements of a quantum logic, i.e., a model for the collection of propositions on a general physical system. The physical importance of this has its origin in the uncertainty principle of Heisenberg. Starting with a logic \({\mathcal L}\), the author constructs a topological space (\({\mathcal L},{\mathcal T})\). The topological \({\mathcal T}\) is considered to be connected, in a sense, with the state of the corresponding physical system. The topology defined in the paper is linked with a finite measure \(\mu\) on \({\mathcal L}\) and the constructed topology is associated with this measure.
Reviewer: N.D.Sengupta


03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
46N99 Miscellaneous applications of functional analysis
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