Exact topological analogs to orthoposets
Peter G. Ovchinnikov · Proceedings of the American Mathematical Society · 1997
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.