 From this, it is not hard to see that, for an algebraic test space \(\mathcal{A}\), the relation \(\sim \) of perspectivity is then an equivalence relation on the set of \(\mathcal{A}\)-events. More than this, if \(\mathcal{A}\) is algebraic, then \(\sim \) is a congruence for the partial binary operation of forming unions of orthogonal events: in other words, for all \(\mathcal{A}\)-events \(A, B\), and \(C, A\sim B\) and \(B\binbot C\) imply that \(A\binbot C\) and \(A\cup C \sim B\cup C\).