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Exact topological analogs to orthoposets

Author: Peter G. Ovchinnikov
Journal: Proc. Amer. Math. Soc. 125 (1997), 2839-2841
MSC (1991): Primary 06C15, 54H10; Secondary 81P10
MathSciNet review: 1415360
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Abstract: An arbitrary orthoposet $E$ is shown to be isomorphic to $(\mathcal E, \subset ,^c)$, $\mathcal E$ being a subbasis of a Hausdorff topological space $\mathcal S$ satisfying 1) $\mathcal S\in \mathcal E$, 2) $\alpha \in \mathcal E\Rightarrow\alpha ^c \in \mathcal E$, and 3) every covering of $\mathcal S$ by elements of $\mathcal E$ possesses an at most 2-element subcovering. The couple $(\mathcal S,\mathcal E)$ turns out to be unique.

References [Enhancements On Off] (What's this?)

  • 1. J. Binder and P. Pták, A representation of orthomodular lattices, Acta Univ. Carolinae 31 (1990), 21-26. MR 92b:06028
  • 2. G. Birkhoff, Lattice theory, AMS, Providence, RI, 1967. MR 37:2638
  • 3. S. Gudder, Stochastic methods in quantum mechanics, North Holland, New York, 1979. MR 84j:81003
  • 4. G. Kalmbach, Orthomodular lattices, Academic Press, London, 1983. MR 85f:06012
  • 5. -, Measures and Hilbert lattices, World Scientific, Singapore, 1986. MR 88a:06013
  • 6. K. Kuratowski, Topology, v. 2, Academic Press, New York, 1968. MR 41:4467
  • 7. P. Pták and S. Pulmannová, Orthomodular structures as quantum logics, Kluwer, Dordrecht, 1991. MR 94d:81018b
  • 8. R. Sikorski, Boolean algebras, Springer, Berlin, 1964. MR 31:2178

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Additional Information

Peter G. Ovchinnikov
Affiliation: Department of Mathematics, Kazan State University, 420008, Kazan, Russia

Keywords: Orthopair, orthoposet, subbasis, zero-dimensional compact topological space
Received by editor(s): April 9, 1996
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1997 American Mathematical Society

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