Multiset Relations and Topologies on Multisets

Multiset is a collection of objects in which the elements are allowed to repeat. The notion of multiset relations and multiset functions are introduced and the concepts in general topology on classical sets are extended to topology on multisets. Partially ordered multisets and their chains and antichains are introduced and the decomposition theorem for partially ordered multisets is obtained. Moreover multiset topologies are generated using multiset relations and to obtain a quasi-discrete multiset topology from a symmetric multiset relation instead of an equivalence multiset relation. Rough multisets are introduced and the relationship between rough multisets and multiset topologies are investigated.

Autorentext

Dr.Girish K P, Asst. Prof., Center for Cyber Security, Amrita Vishwa Vidyapeetham University, India. His areas of research interest are Multiset Theory and Cryptography.Dr Sunil Jacob John, Associate Prof., Dept. of Mathematics, NIT Calicut, India. His areas of research interest are Fuzzy Mathematics, Topology, Multiset and Dimension Theory.