An Intrisic Topology for Orthomodular Lattices

Olivier Brunet

doi:10.1007/s10773-007-9400-8

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An Intrisic Topology for Orthomodular Lattices

Olivier Brunet

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Abstract

We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.

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Olivier Brunet. 2007-02-03. An Intrisic Topology for Orthomodular Lattices. https://doi.org/10.1007/s10773-007-9400-8

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