 Consequence operations are present not only in logic but in many areas of mathematics. Abstract consequence operations are known as closure operators in universal algebra and lattice theory, for instance. In topology the operation that sends a subset of a topological space to its topological closure is a closure operator. In fact, the topologies on a set \(A\) can be identified with the closure operators on \(A\) that satisfy the additional conditions that \(C(\varnothing) = \varnothing\) and \(C(X \cup Y) = C(X) \cup C(Y)\) for all \(X, Y \subseteq A\).