dorsal/arxiv
View SchemaAn Intrisic Topology for Orthomodular Lattices
| Authors | Olivier Brunet |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702025 |
| URL | https://arxiv.org/abs/quant-ph/0702025 |
| DOI | 10.1007/s10773-007-9400-8 |
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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"abstract": "We present a general way to define a topology on orthomodular lattices. We\nshow that in the case of a Hilbert lattice, this topology is equivalent to that\ninduced by the metrics of the corresponding Hilbert space. Moreover, we show\nthat in the case of a boolean algebra, the obtained topology is the discrete\none. Thus, our construction provides a general tool for studying orthomodular\nlattices but also a way to distinguish classical and quantum logics.",
"arxiv_id": "quant-ph/0702025",
"authors": [
"Olivier Brunet"
],
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"doi": "10.1007/s10773-007-9400-8",
"title": "An Intrisic Topology for Orthomodular Lattices",
"url": "https://arxiv.org/abs/quant-ph/0702025"
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