Exact topological analogs to orthoposets

Abstract

An arbitrary orthoposet E is shown to be isomorphic to (ε, C,c ), ε being a subbasis of a Hausdorff topological space S satisfying 1) S ∈ ε, 2) α ∈ αc ∈ ε, and 3) every covering of S by elements of ε possesses an at most 2-element subcovering. The couple (S,ε) turns out to be unique. ε 1997 American Mathematical Society.