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

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

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