Name of mapping from multiset to underlying set

Question

I'd like advice on the most appropriate term for the operation of mapping from a multiset to its underlying set.

In the literature accessible to me in half a day's worth of hunting online, I can find five ways of referring to the underlying set of a multiset (i.e. the multiset's content if the multiplicity of all of its members were set to 1):

1. Underlying set
2. Support
3. Carrier
4. Root
5. Full multisubset

and I can find four terms used for the operation on a multiset of finding the underlying set (reducing all the multiplicities to 1):

1. Unique
2. Duplicate elimination
3. Root
4. Distinct

Is there a preferred term for this operation?