Conversely, any closure operator on some poset gives rise to the Galois connection with lower adjoint being just the corestriction of to the image of (i.e. as a surjective mapping the closure system ). The upper adjoint is then given by the inclusion of into , that maps each closed element to itself, considered as an element of . In this way, closure operators and Galois connections are seen to be closely related, each specifying an instance of the other. Similar conclusions hold true for kernel operators.