Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Exact topological analogs to orthoposets

Author(s): 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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