Closures on partial partitions from closures on sets

Jordens and Sturm investigated the link between closure systems on sets and closure systems on partitions. We extend that study to the wider framework of partial partitions, and highlight better the relation between these two families of closure systems. Then we consider the construction of a closure operator on partial partitions by the iterated application a set operator to the blocks of a partial partition; the resulting closure system fits into our framework.