Ideal convergence of multiset sequences

Abstract

Although elements are written only once in classical set theory, it is possible to find many examples in daily life where an element is repeated more than once in a set and each repetition is indispensable. This situation is an indication of how important multisets are. On the other hand, ideal convergence is a type of convergence that generalizes many convergence types, and it is quite interesting how this convergence type can be defined for multiset sequences and what properties it will provide. For this purpose, in this paper we introduce the ideal convergence of multiset sequences and we investigate some basic algebraic and topological properties of a multiset sequences.