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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Exact topological analogs to orthoposets
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by Peter G. Ovchinnikov PDF
Proc. Amer. Math. Soc. 125 (1997), 2839-2841 Request permission

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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Additional Information
  • Peter G. Ovchinnikov
  • Affiliation: Department of Mathematics, Kazan State University, 420008, Kazan, Russia
  • Email: Petr.Ovchinnikov@ksu.ru
  • Received by editor(s): April 9, 1996
  • Communicated by: Franklin D. Tall
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 2839-2841
  • MSC (1991): Primary 06C15, 54H10; Secondary 81P10
  • DOI: https://doi.org/10.1090/S0002-9939-97-04023-9
  • MathSciNet review: 1415360