Encounter to the Additive Property of Local Function
Abstract
Through this paper we will modify some of the results of [1], [5], [15], [28], [29], [31], [32] and
consequently give the modified results.
Downloads
Download data is not yet available.
References
1. Abbas, F., Pre-local function in ideal topological spaces, Int. J. Adv. Sci. Eng. 8(1), 2085-2089, (2021).
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 β -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. El-Monsef, M. E. A., El-Deeb, S. N. and Mahmoud, R. A., β -open sets and β -continuous mappings, Bull. Fac. Sci. Assiut Univ. 12, 77-90, (1983).
8. Hamlett, T. R., A correction to the paper "semi-open sets and semicontinuityi n topological spaces" by normanl evine, Proceedings of the American Mathematical Society, 49(2), 458-460, (1975).
9. Hamlett, T. R. and Jankovic, D., Ideals in topological spaces and the set operator ψ , Bull. U. M. I. 7(4-B), 863-874, (1990).
10. Hashimoto, H., On the *-topology and its applications, Fundam. Math., 156, 5-10, (1976).
11. Hayashi, E., Topologies de fined by local properties, Mathematische Annalen, 156(3), 205-215, (1964).
12. 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.
13. Islam, Md. M. and Modak, S., Operator associated with the * and ψ operators, Journal of Taibah University for Science,12(4), 444{449, (2018).
14. Jancovic, D. and Hamlett, T. R., New topologies from old via ideal, Amer. Math. Monthly. 97, 295-310, (1990).
15. Khan, M. and Noiri, T., Semi-local functions in ideal topological spaces, Journal of Advanced Research in Pure Mathematics, 2(1), 36-42, (2010).
16. Kuratowski, K., Topologie I, Warszawa, 1933.
17. Levine, N., Semi-open sets and semi-continuity in topological spaces, The American Mathematical Monthly, 70(1), 36-41, (1963).
18. 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).
19. Mistry, S. and Modak, S., ()*p and ψp operator, International Mathematical Forum, 7(2), 89 - 96, (2012).
20. Modak, S., Ideal on beta space, ISST Journal of Mathematics & Computing System, 2(2), 7-11, (2011).
21. Modak, S., Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 82(3), 233-243, (2012).
22. Modak S. and and Bandyopadhyay, C., A note on ψ-operator, Bull. Malays. Math. Sci. Soc. 30(1), 43{48, (2007).
23. Modak S. and and Mistry, S., ()*s and ψs operator, Int. J. Contemp. Math. Sciences, 7(1), 1-8, (2012).
24. Modak, S. and Noiri, T., Some generalizations of locally closed sets, Iranian Journal of Mathematical Sciences and Informatics, 14(1), 159-165, (2019).
25. Modak, S. and Selim, Sk., Set operator and associated functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 70(1), 456-467, (2021).
26. Modak, S. and Selim, Sk., Set operators and associated functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 70(1), 456-467, (2021).
27. Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca. 36(3), 297-312, (1986).
28. Powar, P. L., Noiri, T. and Bhadauria, S., On β -local functions in ideal topological spaces, European Journal Of Pure And Applied Mathematics, 13(4), 758-765, (2020).
29. Theodore J. and Beulah, V., On g β*I-closed sets in ideal topological spaces, Global Journal of Pure and Applied Mathematics, 13(9), 6155-6165, (2017).
30. Vaidyanathaswamy, R., The localisation theory in set-topology, Proc. Indian Acad. Sci. 20(1), 51-61, (1944).
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).
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 β -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. El-Monsef, M. E. A., El-Deeb, S. N. and Mahmoud, R. A., β -open sets and β -continuous mappings, Bull. Fac. Sci. Assiut Univ. 12, 77-90, (1983).
8. Hamlett, T. R., A correction to the paper "semi-open sets and semicontinuityi n topological spaces" by normanl evine, Proceedings of the American Mathematical Society, 49(2), 458-460, (1975).
9. Hamlett, T. R. and Jankovic, D., Ideals in topological spaces and the set operator ψ , Bull. U. M. I. 7(4-B), 863-874, (1990).
10. Hashimoto, H., On the *-topology and its applications, Fundam. Math., 156, 5-10, (1976).
11. Hayashi, E., Topologies de fined by local properties, Mathematische Annalen, 156(3), 205-215, (1964).
12. 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.
13. Islam, Md. M. and Modak, S., Operator associated with the * and ψ operators, Journal of Taibah University for Science,12(4), 444{449, (2018).
14. Jancovic, D. and Hamlett, T. R., New topologies from old via ideal, Amer. Math. Monthly. 97, 295-310, (1990).
15. Khan, M. and Noiri, T., Semi-local functions in ideal topological spaces, Journal of Advanced Research in Pure Mathematics, 2(1), 36-42, (2010).
16. Kuratowski, K., Topologie I, Warszawa, 1933.
17. Levine, N., Semi-open sets and semi-continuity in topological spaces, The American Mathematical Monthly, 70(1), 36-41, (1963).
18. 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).
19. Mistry, S. and Modak, S., ()*p and ψp operator, International Mathematical Forum, 7(2), 89 - 96, (2012).
20. Modak, S., Ideal on beta space, ISST Journal of Mathematics & Computing System, 2(2), 7-11, (2011).
21. Modak, S., Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 82(3), 233-243, (2012).
22. Modak S. and and Bandyopadhyay, C., A note on ψ-operator, Bull. Malays. Math. Sci. Soc. 30(1), 43{48, (2007).
23. Modak S. and and Mistry, S., ()*s and ψs operator, Int. J. Contemp. Math. Sciences, 7(1), 1-8, (2012).
24. Modak, S. and Noiri, T., Some generalizations of locally closed sets, Iranian Journal of Mathematical Sciences and Informatics, 14(1), 159-165, (2019).
25. Modak, S. and Selim, Sk., Set operator and associated functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 70(1), 456-467, (2021).
26. Modak, S. and Selim, Sk., Set operators and associated functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 70(1), 456-467, (2021).
27. Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca. 36(3), 297-312, (1986).
28. Powar, P. L., Noiri, T. and Bhadauria, S., On β -local functions in ideal topological spaces, European Journal Of Pure And Applied Mathematics, 13(4), 758-765, (2020).
29. Theodore J. and Beulah, V., On g β*I-closed sets in ideal topological spaces, Global Journal of Pure and Applied Mathematics, 13(9), 6155-6165, (2017).
30. Vaidyanathaswamy, R., The localisation theory in set-topology, Proc. Indian Acad. Sci. 20(1), 51-61, (1944).
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
2025-08-24
Issue
Section
Research Articles
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
