On Multiset Minimal Structure Topological Space

Abstract

In this article we established the concept of multi-continuity in minimal structure spaces (in short $\mathscr{M}$ space) and the notion of product minimal space in multiset topological space. Continuity between $\mathscr{M}$-space, generalized multiset topology and multiset ideal topological spaces. We have investigated some basic properties of $\mathscr{M}$–continuity in multiset topological space, such as composition of $\mathscr{M}$–continuous functions, product of $\mathscr{M}$–continuous functions in product multiset topological space etc.

Keywords

• Multi set
• Multiset topology
• Minimal Structure
• Multiset semi-open set
• Multiset product space
• Generalized multiset
• Ideal

References

1. Reference1 Blizard, W.D.: Multiset Theory. Notre Dame Jour. Logic, 30, 36-65(1989).
2. Reference2 Blizard, W.D.: The development of multiset theory. Modern Logic. 1, 319-352(1991).
3. Reference3 Csaszar, A.: Generalized topology, generalized continuity. Acta Math. Hungar., 96(4), 351-357(2002).
4. Reference4 Dembre, V.: New axioms in topological spaces. Int. Jour. Comp. Appl. Tech. and Research, 7(3): 109-113(2018).
5. Reference5 El-Sheikh, S., Omar, R., Raafat, M.: Separation axioms on multiset topological Space. jour. new theory, 7, 11-21(2015).
6. Reference6 Girish, K.P., John, S.J.: Relations and functions in multiset context. Inf. Sci., 179(6), 758-768(2009).
7. Reference7 Girish, K.P., John, S.J.: Multiset topologies induced by multiset relations. Information Sciences, 188, 298-313(2012).
8. Reference8 Kanibir, A., Reilly, I.L.: Generalized continuity for multifunctions. Acta 117 Math. Hungar., 122(3), 283-292(2009).

9. Reference9 Mahanta. S. Samanta S.K.: Compactness in Multiset Topology. Inter. Jour. Math. Trends and Tech. 47(4), 275-288(2017).
10. Reference10 Powar, P.L. Rajak, K.: Ultra-Separation Axioms in Generalized Topological Space. Inte. Jour. Electro Comput. World Know. Inter. 1(4), 34-40(2011).
11. Reference11 Shravan, K., Tripathy, B.C.: Generalised closed sets in multiset topological spaces. Proyecciones Jour. Math., 37(2), 223-237(2018).
12. Reference12 Shravan, K., Tripathy, B.C.: Multiset ideal topological spaces and local functions. Proyecciones Jour. Math., 37(4), 699-711(2018).
13. Reference13 Shravan, K., Tripathy, B.C.: Multiset mixed topological space. Soft Comput, 23, 9801-9805(2019).
14. Reference14 Shravan, K., Tripathy, B.C.: Multiset ideal topological spaces and Kuratowski closure operator, Bull. Univ. Transilvania Brasov, Series III: Mathematics, Informatics, Physics, 13(62)(1), 273-284(2020).
15. Reference15 Shravan, K., Tripathy, B.C.: Metrizability of multiset topological spaces, Bull. Univ. Transilvania Brasov, Series III: Mathematics, Informatics, Physics, 13(62)(2), 683-696(2020).
16. Reference16 Tripathy, B.C., Ray, G.C.: Mixed fuzzy ideal topological spaces; Applied Mathematics and Computations; 220, 602-607(2013).
17. Reference17 Tripathy, B.C., Ray, G.C.: On $\delta$-continuity in mixed fuzzy topological spaces, Boletim da Sociedade Paranaense de Matemática, 32(2), 175-187)(2014).
18. Reference18 Tripathy, B.C., Das, R.: Multiset Mixed Topological Space. Transactions of A. Razmadze Mathematical Institute, (Accepted)
19. Reference19 Tripathy, B.C., Ray, G.C.: Weakly continuous functions on mixed fuzzy topological spaces; Acta Scientiarum. Technology, 36(2), 331-335(2014).
20. Reference20 Tripathy, B.C., Ray, G.C.: Fuzzy $\delta-I$-continuity in mixed fuzzy ideal topological spaces, Journal of Applied Analysis, 24(2), 233-239(2018).