Multiset topologies induced by multiset relations

Multiset topology is a collection of multisets which satisfies the axioms of topology. In this paper, multiset topologies are obtained using binary multiset relations. The relationship between multiset topologies is investigated and some of the properties of these multiset topologies are proved. The quasi-discrete multiset topology is obtained from a symmetric multiset relation instead of an equivalence multiset relation and several examples are given to indicate counter connections. Finally, the rough multiset is introduced and the multiset topology induced by a multiset relation is used to generalize the rough multiset concept.