# REDUNDANCY OF MULTISET TOPOLOGICAL SPACES

Document Type : Research Paper

Author

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

Abstract

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.

Keywords

#### References

[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,
arXiv:1501.07193.
[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),
23{37.
[15] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338{353.