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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.


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  • 1. Jiří Binder and Pavel Pták, A representation of orthomodular lattices, Acta Univ. Carolin. Math. Phys. 31 (1990), no. 1, 21–26 (English, with Russian and Czech summaries). MR 1098124
  • 2. Garrett Birkhoff, Lattice theory, Third edition. American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
  • 3. Stanley P. Gudder, Stochastic methods in quantum mechanics, North-Holland, New York-Oxford, 1979. North-Holland Series in Probability and Applied Mathematics. MR 543489
  • 4. Gudrun Kalmbach, Orthomodular lattices, London Mathematical Society Monographs, vol. 18, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1983. MR 716496
  • 5. G. Kalmbach, Measures and Hilbert lattices, World Scientific Publishing Co., Singapore, 1986. MR 867884
  • 6. K. Kuratowski, Topology. Vol. II, New edition, revised and augmented. Translated from the French by A. Kirkor, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe Polish Scientific Publishers, Warsaw, 1968. MR 0259835
  • 7. Pavel Pták and Sylvia Pulmannová, Orthomodular structures as quantum logics, Fundamental Theories of Physics, vol. 44, Kluwer Academic Publishers Group, Dordrecht, 1991. Translated from the 1989 Slovak original by the authors. MR 1176314
  • 8. Roman Sikorski, Boolean algebras, Second edition. Ergebnisse der Mathematik und ihrer Grenzgebiete, NeueFolge, Band 25, Academic Press Inc., New York; Springer-Verlag, Berlin-New York, 1964. MR 0177920

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Additional Information

Peter G. Ovchinnikov
Affiliation: Department of Mathematics, Kazan State University, 420008, Kazan, Russia
Email: Petr.Ovchinnikov@ksu.ru

DOI: https://doi.org/10.1090/S0002-9939-97-04023-9
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