Interior and neighbourhood

The notion of interior operator is intimately related to that of neighbourhood operator. This relationship is presented here in the form of an adjunction or Galois connection, in the sense that on an object (a space) X  , the neighbourhood operator νXνX admits a right adjoint which agrees with its associated interior operator iXiX on the subobjects (subspaces). We establish this one-to-one correspondence and present some consequences of this relation.