New separation axiom in multiset topology
DOI:
https://doi.org/10.5269/bspm.66920Resumo
In this article we introduce some M-topological operators called multiset kernel and multiset shell operators. Then we define a new separation axiom termed as multiset $T_{D}$- spaces and investigate some of its basic properties. It is observed that this space precisely lies between multiset $T_0$ and multiset $T_1$-spaces. Also, we characterize multiset $T_0$, $T_1$ and $T_D$-spaces in the light of the mentioned operators.Referências
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2. W. D. Blizard, The development of multiset theory, Modern Logic, 1(4)(1991) 319-352
3. M. M El-Sharkasy and M. S Badr, Modeling DNA and RNA mutation using mset and topology. International Journal of Biomathematics 11(04)(2018) 1850058
4. M. M. El-Sharkasy, W. M. Fouda and M. S. Badr, Multiset topology via DNA and RNA mutation. Mathematical Methods in the Applied Sciences, 41(15)(2018) 5820-5832
5. A. Ghareeb, Redundancy of multiset topological spaces, Iran. J. Fuz. Sys., 14(2017) 163–168
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8. K. P. Girish and S. J. John, On multiset topologies, Theory Appl. Math. Comput. Sci. 2(2012) 37-52
9. J. L. Hickman, A note on the concept of multiset, Bull. Austral. Math. Soc., 22 (1980) 211–217
10. A. Jakaria, Note on multiset topologies, Annals Fuzzy Math Inform, 10(5)(2015) 825-827
11. S. P. Jena, S. K. Ghosh and B. K. Tripathy, On the theory of bags and lists, Information Sciences 132(2001) 241–254
12. P. R. Kumar and S. J. John, On redundancy, separation, and connectedness in multiset topological spaces, AIMS Math 5(3)(2020) 2484-2499
13. P. R. Kumar, S. J. John and S. Samanta, Compactness and subspace M-topologies, Soft Computing, 26(2022) 4115-4122
14. S. Mahanta and S. K. Samanta, Compactness in multiset topology, Int. J. Math. Trends Tech. (IJMTT), 47 (2017) 275–282
15. P. M. Mahalakshmi and P. Thangavelu, M-Connectedness in M-Topology, Internat. Jour. Pure Appl. Math., 106 (8)(2016) 21-25
16. P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, J. Fuzzy Math., 9(3)(2001) 589-602
17. D. Molodstov, Soft set theory-first results, Comp. Math. Appli., 37(1999) 19–31
18. Z. Pawlak, Rough sets, Int. J. Comp. Inf. Sci., 11(1982) 341–356
19. G. C. Ray and S. Dey, Mixed multiset topological space and separation axioms, Indian J Pure Appl Math, 53(1)(2022) 92-99
20. S. E. Sheikh, O. Rajab and M. Raafat, Separation axioms on multiset topological space. Journal of New Theory (7)(2015) 11-21
21. K. Shravan and B. C. Tripathy, Generalised closed sets in multiset topological space, Proyecciones J. Math. 37(2)(2018) 223-237
22. K. Shravan and B. C. Tripathy, Multiset ideal topological spaces and local function, Proyecciones J. Math. 37(4)(2018) 699-711
23. K. Shravan and B. C. Tripathy, Multiset mixed topological space, Soft Computing, 23(2019) 9801-9805
24. F. Smarandache, A unifying field in logics, neutrosophy: neutrosophic probability, set and logic. Rehoboth: American Research Press (1998)
25. R. R. Yager, On the theory of bags, Int. J. Gen. Syst. 13(1) (1986) 23–37
26. L. A. Zadeh, Fuzzy sets, Inform. and Control, 8(1965) 338-353
2. W. D. Blizard, The development of multiset theory, Modern Logic, 1(4)(1991) 319-352
3. M. M El-Sharkasy and M. S Badr, Modeling DNA and RNA mutation using mset and topology. International Journal of Biomathematics 11(04)(2018) 1850058
4. M. M. El-Sharkasy, W. M. Fouda and M. S. Badr, Multiset topology via DNA and RNA mutation. Mathematical Methods in the Applied Sciences, 41(15)(2018) 5820-5832
5. A. Ghareeb, Redundancy of multiset topological spaces, Iran. J. Fuz. Sys., 14(2017) 163–168
6. K. P. Girish and S. J. John, Relations and functions in multiset context, Information Sciences 179(2009) 758–768
7. K. P. Girish and S. J. John, Multiset topologies induced by multiset relations, Information Sciences 188(2012) 298–313
8. K. P. Girish and S. J. John, On multiset topologies, Theory Appl. Math. Comput. Sci. 2(2012) 37-52
9. J. L. Hickman, A note on the concept of multiset, Bull. Austral. Math. Soc., 22 (1980) 211–217
10. A. Jakaria, Note on multiset topologies, Annals Fuzzy Math Inform, 10(5)(2015) 825-827
11. S. P. Jena, S. K. Ghosh and B. K. Tripathy, On the theory of bags and lists, Information Sciences 132(2001) 241–254
12. P. R. Kumar and S. J. John, On redundancy, separation, and connectedness in multiset topological spaces, AIMS Math 5(3)(2020) 2484-2499
13. P. R. Kumar, S. J. John and S. Samanta, Compactness and subspace M-topologies, Soft Computing, 26(2022) 4115-4122
14. S. Mahanta and S. K. Samanta, Compactness in multiset topology, Int. J. Math. Trends Tech. (IJMTT), 47 (2017) 275–282
15. P. M. Mahalakshmi and P. Thangavelu, M-Connectedness in M-Topology, Internat. Jour. Pure Appl. Math., 106 (8)(2016) 21-25
16. P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, J. Fuzzy Math., 9(3)(2001) 589-602
17. D. Molodstov, Soft set theory-first results, Comp. Math. Appli., 37(1999) 19–31
18. Z. Pawlak, Rough sets, Int. J. Comp. Inf. Sci., 11(1982) 341–356
19. G. C. Ray and S. Dey, Mixed multiset topological space and separation axioms, Indian J Pure Appl Math, 53(1)(2022) 92-99
20. S. E. Sheikh, O. Rajab and M. Raafat, Separation axioms on multiset topological space. Journal of New Theory (7)(2015) 11-21
21. K. Shravan and B. C. Tripathy, Generalised closed sets in multiset topological space, Proyecciones J. Math. 37(2)(2018) 223-237
22. K. Shravan and B. C. Tripathy, Multiset ideal topological spaces and local function, Proyecciones J. Math. 37(4)(2018) 699-711
23. K. Shravan and B. C. Tripathy, Multiset mixed topological space, Soft Computing, 23(2019) 9801-9805
24. F. Smarandache, A unifying field in logics, neutrosophy: neutrosophic probability, set and logic. Rehoboth: American Research Press (1998)
25. R. R. Yager, On the theory of bags, Int. J. Gen. Syst. 13(1) (1986) 23–37
26. L. A. Zadeh, Fuzzy sets, Inform. and Control, 8(1965) 338-353
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2025-01-21
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