Pick some mathematical object that has an underlying set, for instance a group, ring, vector space, etc. For any subset of , let be the smallest subobject of that contains , i.e. the subgroup, subring or subspace generated by . For any subobject of , let be the underlying set of . (We can even take to be a topological space, let the closure of , and take as "subobjects of " the closed subsets of .) Now and form a monotone Galois connection between subsets of and subobjects of , if both are ordered by inclusion. is the lower adjoint.