Multisets and Multiset Mappings
- 270 Downloads
Multisets are collections of elements which may appear with multiplicity. We review the multiplicity function and cardinality, and we introduce the notion of filter to extract the distinct elements in a multiset. We define a notion of outer limit for sequences of multisets, and we define and develop “multiset mappings” that take multisets to multisets. We introduce a generalized continuity property for multiset mappings (called calmness) that relies on choices of pre-distance functions, and we investigate how this property generalizes a similar property for set-valued mappings. We define a generalized derivative for multiset mappings and use it to characterize calmness.
- 13.Knuth, D.E.: Seminumerical Algorithms. The Art of Computer Programming, vol. 2, 3rd edn. Addison-Wesley, Boston (1998)Google Scholar
- 20.Robinson, S.M.: Generalized equations and their solutions. I. Basic theory. In: Point-to-Set Maps and Mathematical Programming. Mathematical Programming Studies, vol. 10, pp. 128–141. Springer, Berlin (1979)Google Scholar