Multisets and Multiset Mappings
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.
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