Some properties of \(R_i\)-axioms via multi-set topological spaces
Volume 34, Issue 3, pp 257--267
https://dx.doi.org/10.22436/jmcs.034.03.05
Publication Date: March 22, 2024
Submission Date: December 26, 2023
Revision Date: February 13, 2024
Accteptance Date: February 15, 2024
Authors
S. Saleh
- Department of Mathematics, Hodeidah University, Hodeidah, Yemen.
- Department of Computer Science, Cihan University-Erbil, Erbil, Iraq.
J. Al-Mufarrij
- Department of Mathematics, Women section, King Saud University, Riyadh 12372, KSA.
A. M. Alzubaidi
- Department of Mathematics, Al-Qunfudhah University College, Umm Al-Qura University, KSA.
A. Al-Salemi
- Department of Mathematics, Hodeidah University, Hodeidah, Yemen.
Abstract
multi-set are sets that are allowed to have repeated members, that is a multi-set \(\mathcal{M}\) on a set \(U\) is a count function \(C_\mathcal{M}\) from \(U\) to non-negative numbers. This study focuses on introducing and analyzing two new classes of separation axioms named, \(\mathcal{M}\)-\(R_0\) and \(\mathcal{M}\)-\(R_1\) in the context of multi-set topological spaces by utilizing the concepts of distinct \(\mathcal{M}\)-singletons and m-closure operator, investigating certain properties and characterizing them with some illustrative examples. Relationships with other \(\mathcal{M}\)-separation axioms are explored, and it is demonstrated that \(M\)-\(R_0\) and \(M\)-\(R_1\) are special cases of \(\mathcal{M}\)-regularity. Furthermore, we show that in the context of compact \(\mathcal{M}\)-spaces, \(\mathcal{M}\)-\(R_1\) is equivalent to whole \(\mathcal{M}\)-regularity. Finally, the hereditary property of these classes is examined.
Share and Cite
ISRP Style
S. Saleh, J. Al-Mufarrij, A. M. Alzubaidi, A. Al-Salemi, Some properties of \(R_i\)-axioms via multi-set topological spaces, Journal of Mathematics and Computer Science, 34 (2024), no. 3, 257--267
AMA Style
Saleh S., Al-Mufarrij J., Alzubaidi A. M., Al-Salemi A., Some properties of \(R_i\)-axioms via multi-set topological spaces. J Math Comput SCI-JM. (2024); 34(3):257--267
Chicago/Turabian Style
Saleh, S., Al-Mufarrij, J., Alzubaidi, A. M., Al-Salemi, A.. "Some properties of \(R_i\)-axioms via multi-set topological spaces." Journal of Mathematics and Computer Science, 34, no. 3 (2024): 257--267
Keywords
- m-sets
- closed m-sets
- m-singletons sets
- m-closure operator
- \(\mathcal{M}\)-topology
MSC
References
-
[1]
W. D. Blizard, multi-set theory, Notre Dame J. Formal Logic, 30 (1989), 36–66
-
[2]
W. D. Blizard, The development of multi-set theory, Modern Logic, Mod. Log., 1 (1991), 319–352
-
[3]
W. D. Blizard, Dedekind multi-sets and function shells, Theoret. Comput. Sci., 110 (1993), 79–98
-
[4]
M. M. El-Sharkashy, W. M. Fouda, M. S. Badr, Multi-set topology via DNA and RNA mutation, Math. Methods Appl. Sci., 41 (2018), 5820–5832
-
[5]
S. A. El-Sheikh, R. A. K. Omar, M. Raafat, -operation in M-topological space, Gen. Math. Notes, 27 (2015), 40–54
-
[6]
S. A. El-Sheikh, R. A. K. Omar, M. Raafat, Separation axioms on multi-set topological space, J. New Theory, 7 (2015), 11–21
-
[7]
S. A. El-Sheikh, R. A. K. Omar, M. Raafat, Supra M-topological space and decompositions of some types of supra m-sets, Int. J. Math. Trends Technol., 20 (2015), 11–24
-
[8]
K. P. Girish, J. S. Jacob, On multi-set topologies, Theory Appl. Math. Comput. Sci., 2 (2012), 37–52
-
[9]
K. P. Girish, S. J. John, Rough multi-sets and information multi systems, Adv. Decis. Sci., 2011 (2011), 1–17
-
[10]
K. P. Girish, S. J. John, Multi-set topologies induced by multi-set relations, Inform. Sci., 188 (2012), 298–313
-
[11]
A. M. Ibrahim, D. Singh, J. N. Singh, An outline of multi-set space algebra, Int. J. Algebra, 5 (2011), 1515–1525
-
[12]
S. P. Jena, S. K. Ghosh, B. K. Tripathy, On the theory of bags and lists, Inform. Sci., 132 (2001), 241–254
-
[13]
A. Kandil, O. A. Tantawy, S. A. El-Sheikh, A. Zakaria, Multiset proximity spaces, J. Egyptian Math. Soc., 24 (2016), 562–567
-
[14]
R. Kumar P, S. J. John, On redundancy, separation and connectedness in multi-set topological spaces, AIMS Math., 5 (2020), 2484–2499
-
[15]
P. M. Mahalakshmi, P. Thangavelu, M-connectedness in M-topology, Int. J. Pure Appl. Math., 106 (2016), 21–25
-
[16]
S. Mahanta, S. K. Samanta, Compactness in multi-set topology, Int. J. Math. Trends Technol., 47 (2017), 275–282
-
[17]
K. Shravan, B. C. Tripathy, Generalized closed sets in multi-set topological space, Proyecciones, 37 (2018), 223–237
-
[18]
K. Shravan, B. C. Tripathy, Multi-set ideal topological spaces and local functions, Proyecciones, 37 (2018), 699–711
-
[19]
D. Singh, A. M. Ibrahim, T. Yohana, J. N. Singh, An overview of the applications of multi-sets, Novi Sad J. Math., 37 (2007), 73–92
-
[20]
D. Singh, J. N. Singh, Some combinatorics of multi-sets, Internat. J. Math. Ed. Sci. Tech., 34 (2003), 489–499
-
[21]
A. Syropoulos, Mathematics of multi-sets in multi-set processing, Springer-Verlag, Berlin Heidelberg, 2235 (2001), 347–358
-
[22]
R. R. Yager, On the theory of bags, Internat. J. Gen. Systems, 13 (1987), 23–37
-
[23]
Y. Yang, X. Tan, C. Meng, the multi-fuzzy soft set and its application in decision making, Appl. Math. Model., 37 (2013), 4915–4923
-
[24]
A. Zakaria, S. J. John, K. P. Girish, Multi-set Filters, J. Egyptian Math. Soc., 27 (2019), 12 pages
