Multiset proximity spaces

A multiset is a collection of objects in which repetition of elements is essential. This paper is an attempt to explore the theoretical aspects of multiset by extending the notions of compact, proximity relation and proximal neighborhood to the multiset context. Examples of new multiset topologies, open multiset cover, compact multiset and many identities involving the concept of multiset have been introduced. Further, an integral examples of multiset proximity relations are obtained. A multiset topology induced by a multiset proximity relation on a multiset M has been presented. Also the concept of multiset δ- neighborhood in the multiset proximity space which furnishes an alternative approach to the study of multiset proximity spaces has been mentioned. Finally, some results on this new approach have been obtained and one of the most important results is: every T4- multiset space is semi-compatible with multiset proximity relation δ on M (Theorem 5.10).