Document Type : Research Paper


Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt


In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^\star(U),\sqsubseteq)$ and $(Ds(\varphi(U)),\subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.


[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87{96.
[2] W. D. Blizard, Multiset theory, Notre Dame J. Formal Logic, 30(1) (1988), 36{66.
[3] S. A. El-Sheikh, R. A. K. Omar and M. Raafat,
-operation in m-topological space, Gen.
Math. Notes, 7(1) (2015), 40{54.
[4] S. A. El-Sheikh, R. A. K. Omar and M. Raafat, Separation axioms on multiset topological
space, Journal of New Theory, 7 (2015), 11{21.
[5] K. P. Girish and J. S. Jacob, On multiset topologies, Theory and Applications of Mathematics
and Computer Science, 2(1) (2012), 37{52.
[6] K. P. Girish and S. J. John, Transactions on rough sets XIV, Springer Berlin Heidelberg,
Berlin, Heidelberg, (2011), Ch. Rough Multiset and Its Multiset Topology, 62{80.
[7] K. P. Girish and S. J. John, Multiset topologies induced by multiset relations, Information
Sciences, 188 (2012), 298{313.
[8] A. Kandil, O. Tantawy, S. El-Sheikh and A. Zakaria, Multiset proximity spaces, Journal of
Egyptian Mathematical Society, 24(4) (2016), 562-567.
[9] P. M. Mahalakshmi and P. Thangavelu, m-connectedness in m-topology, International Journal
of Pure and Applied Mathematics, 106(8) (2016), 21-25.
[10] J. Mahanta and D. Das, Boundary and exterior of a multiset topology, ArXiv e-prints,
[11] D. Molodtsov, Soft set theory- rst results, Computers and Mathematics with Applications,
37 (45) (1999), 19{31.
[12] F. G. Shi and B. Pang, Redundancy of fuzzy soft topological spaces, Journal of Intelligent and
Fuzzy Systems, 27 (4) (2014), 1757{1760.
[13] F. G. Shi and B. Pang, A note on soft topological spaces, Iranian Journal of Fuzzy Systems,
12 (5) (2015), 149{155.
[14] R. R. Yager, On the theory of bags, International Journal of General Systems, 13 (1986),
[15] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338{353.