A study on multiset and multi-real number system and its use to develop metric in the multiset context

Abstract

 In this paper, we present an alternative development of multiset theory through the notions of
 the general multiset, the Q+-multiset, and N-multiset. We further propose the notion of a multi-real number
 system. Several properties of the general multiset, the Q+-multiset, N-multiset, and the multi-real number
 system are systematically explored. Also we use the multi-real number system to introduce the concept of
 multi-metric space, extending traditional metric space concepts such as distance, neighbourhood, open ball and
 open set to the context of multisets, and investigate its fundamental topological properties. This study offers a
 new perspective on multiset theory and provides a foundation for further research in algebraic and topological
 structures enriched by multiplicity.

DOI: 10.5281/zenodo.17102647