I describe, for each infinite cardinal \(\kappa\), an operator \(S_{\kappa}\) with the properties (i) for any family \({\mathcal A}\) of sets, \({\mathcal A}\subseteq S_{\kappa}({\mathcal A})=S_{\kappa}(S_{\kappa}({\mathcal A}))\) and \(S_{\kappa}({\mathcal A})\) is closed under \(\kappa\)-unions and \(\kappa\)-intersections, (ii) if (X,\({\mathcal T})\) is a topological space of weight at most \(\kappa\), and \({\mathcal H}\) is the family of open sets in \(\kappa^{\kappa}\times X\), then there is a set \(B\in S_{\kappa}({\mathcal H})\) such that \(S_{\kappa}({\mathcal T})\) is precisely the set of vertical sections of B, (iii) if (X,\(\Sigma\),\(\mu)\) is a complete \(\kappa^+\)- additive probability space, then \(S_{\kappa}(\Sigma)=\Sigma\), (iv) \(S_{\omega}\) is the usual Souslin operation S; generally \(S_{\kappa}\) has many of the properties one seeks in a generalization of S. (The particular advance I claim is that \(S_{\kappa}({\mathcal A})\) is always closed under \(\kappa\)-intersections, not just countable intersections.) I give applications in measure theory and general topology.