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" which includes empty set(s)?


(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 to the argument.)



Terminology for a partition of a set which includes empty sets
In Bourbaki's terminology the elements of a partition may be empty (cf. E.II.4.7).


