Additivity of local function and dynamical system
Additivity of local function and dynamical system
Abstract
The study of local function in topological spaces is remarkable. Various branches have been developed through this study. In this paper, we further consider the local function and exploring the various properties of the same by considering some generalized open sets. In this situation some of the properties of local function fails to hold due to the finite intersection property of the topology. Due to this outcome, we are investigating the situation of dynamical system and Topological Transitivity.
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References
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2. Al-Omari A. and Noiri T., Local closure functions in ideal topological spaces, Novi Sad J. Math., 43, 139-149, (2013).
3. Andrijevic D. , Semi-preopen sets. Mat. Vesnik, 38, 24-32, (1986).
4. Andrijevic D., On b-open sets. Mat. Vesnik, 48, 59-64, (1996).
5. Beulah V., Theodore J. and Premalatha D., Notions of -Closure Compatible Topology with an Ideal, Bol. Soc. Paran. Mat., 41 (3s), 1-11, (2023).
6. Dontchev J., Idealization of Ganster-Reilly decomposition theorems, arXiv:math/9901017v1 [math.GN], 5 Jan 1999.
7. Dontchev J., Ganster M. and Rose D., Ideal resolvability, Topol. Appl., 93, 1-16, (1999).
8. El-Monsef M. E. A., El-Deeb S. N. and Mahmoud R. A., -open sets and -continuous mappings, Bull. Fac. Sci. Assiut Univ., 12, 77-90, (1983).
9. Hamlett T. R. and Jankovic D., Ideals in topological spaces and the set operator , Bull. U. M. I. 7(4-B), 863-874, (1990).
10. Islam Md. M. and Modak S., Second approximation of local functions in ideal topological spaces, Acta et Commentationes Universitatis Tartuensis de Mathematica, 22 (2), 245-256, (2018).
11. Jancovi´c D., Hamlett T. R., New topologies from old via ideal, Amer. Math. Monthly, 97, 295-310, (1990).
12. Khan M., Noiri T., Semi-local functions in ideal topological spaces, J. adv. res. pure math., 2(1), 36-42, (2010).
13. Khtaun K., Al-Omari A., Acharjee S. and Modak S., On associated functions and lters, Advances in Topology, Dynamical Systems and Interdisciplinary Apllications (Edited Book Chapter), Springer, accepted.
14. Kuratowski K., Topology, Vol I. Academic Press, New York, (1966).
15. Levine N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1), 36-41, (1963).
16. Mashhour A. S., El-Monsef M. E. A. and El-Deeb S. N., On precontinuous and week precontinuous mappings. Proc. Math. Phys. Soc. Egypt., 53, 47-53, (1982).
17. Mistry S. and Modak S., ()^p and \psi_p operator, Int. Math. Forum, 7(2), 89-96, (2012).
18. Modak S. and Mistry S., ()^s and \psi_s operator, Int. J. Contemp. Math. Sciences, 7(1), 1-8, (2012).
19. Modak S. and Selim S., Set operator and associated functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 70(1), 456-467, (2021).
20. Modak S. and Bandyopadhyay C., A note on -operator, Bull. Malays. Math. Sci. Soc., 30(1), 43{48, (2007).
21. Modak S. and Bandyopadhyay C., -topology and generalized open sets, Soochow J. Math., 32(2), 201-210, (2006).
22. Modak S., Some New Topologies on Ideal Topological Spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 82, 233-243, (2012).
23. Modak S., Ideal on beta space, ISST Journal of Mathematics & Computing System, 2(2), 7-11, (2011).
24. Natkaniec T., On I-continuity and I-semicontinuity points, Math. Slovaca, 36(3), 297-312, (1986).
25. Njastad O., On some classes of nearly open sets, Paci c J. Math, 15, 961-970, (1965).
26. Powar P. L., Noiri T. and Bhadauria S., On -local functions in ideal topological spaces, Eur. j. pure appl. math., 13(4), 758-765, (2020).
27. Selim S., Islam Md M. and Modak S., Common properties and approximations of local function and set operator, Cumhuriyet Sci. J., 41(2), 360-368, (2020).
28. Theodore J. and Beulah V., On g \beta^*I-closed sets in Ideal Topological Spaces, Glob. J. Pure Appl. Math., 13 (9), 6155-6165, (2017).
29. Vaidyanathaswamy R., Set topology, Chelsea Publishing Company, (1960).
30. Yalaz F. and Kaymakci A. K., A new local function and a new compatibility type in ideal topological spaces, AIMS Mathematics, 8(3), 7097-7114, (2024).
31. Yalaz F. and Kaymakci A. K., Weak Semi-Local Functions in Ideal Topological Spaces, Proceedings of International Conference on Mathematics and Mathematics Education (ICMME 2019), Turk. J. Math. Comput. Sci. 11 (Special Issue), 137-140, (2019).
32. Yalaz F. and Kaymakci A. K., New topologies from obtained operators via weak semi-local function and some comprisons, Filomat 35:15, 5073-5081, (2021).
Published
2025-08-13
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