We investigate the application of Galois connections to the identification of frequent item sets, a central problem in data mining. Starting from the notion of closure generated by a Galois connection, we define the notion of extended closure, and we use these notions to improve the classical Apriori algorithm. Our experimental study shows that in certain situations, the algorithms that we describe outperform the Apriori algorithm. Also, these algorithms scale up linearly. 1 C.S.Calude and G.Stefanescu (eds.). Automata, Logic, and Computability. Special issue dedicated to Professor Sergiu Rudeanu Festschrift.