An Intrisic Topology for Orthomodular Lattices

Details An Intrisic Topology for Orthomodular Lattices An Intrisic Topology for Orthomodular Lattices

2007-02-03

arxiv.org/abs/quant-ph/0702025v1

Physics

Quantum Physics

Under submission to the International Journal of Theoretical Physics

Scientific paper

10.1007/s10773-007-9400-8

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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