Mostly I see a partition of a set A defined as a collection of non-empty disjoint sets whose union is A.
I see one reference that allows empty sets to be included in the partition: ("Potter, M. "Set theory and its philosophy", 2004, Oxford University Press, p. 130) "Definition. A collection B of subsets of A is a partition of A if each element of A belongs to exactly one element of B.
Is there some commonly used terminology to refer to a "partition" including empty sets ?
(The context: a set of injections on the sets of a "partition" of A mapping to the set C comprises a bijection iff their images form a "partition" of C. Clearly this is true if empty sets map to empty sets, but it gets somewhat unwieldy to keep adding this in.)