In this paper it is proved that G(Q,P)(the set of all Galois connections of P into Q) is a meet semilattice if and only if both P and Q are meet semilattices and in this case, the meet operation in G(Q,P) is point-wise and P and Q are isomorphic to meet subsemilattices of G(Q,P). © 2020 Forum-Editrice Universitaria Udinese SRL. All rights reserved.