Bounds of substructures of partially ordered multisets

Abstract

Multiset theory naturally extends the classical set theory by considering the number of times an object occurs in a given collection. This work studies notions of bounds on an ordered multiset. The ordered multiset structure is obtained via the ordering induced by the underlying base set, which is assumed to be partially ordered. Analogous concepts of infimum and supremum are defined on substructures of the ordered multiset. In the sequel, some examples are outlined and new results are established on the ordered multiset structure.