On Multi Points of Multisets

Abstract

This paper presents a review of operations on collections of multi-points of multisets involving the addition, union, intersection, difference, symmetric difference, complement, arithmetic multiplication, raising to arithmetic power and scalar multiplication. Furthermore, some algebraic properties of these operations such as commutativity, idempotency, associativity, distributivity and De Morgan’s laws are studied. The concept of a root set multi-point collection of a multipoint collection is examined under union and intersection of such collections.