Function Spaces under Various Operators
Resumo
Various topologies on the function space Y^X will be determined through this paper. To do
this, application of generalized open sets will be discussed. Topological ideal is also an applicable part to
determine the topologies on Y^X. Topological group and the continuous functions will be helpful to determine
the topologies on Y^X (or C(X, Y )). This paper also discusses the huge changes of the topologies on Y^X by
the small displacement of the generalized open sets from the space Y.
Downloads
Não há dados estatísticos.
Referências
1. M. E. Abd El-Monsef, R. A. Mahmoud and A. A. Nasef, Almost-I-openness and almost-I continuity, J. Egypt. Math.Soc. 7 (1999), no. 2, 191-200.
2. Al-omari, A. and Noiri, T., Local closure functions in ideal topological spaces, Novi Sad J. Math. 12(2), 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. Arhangel'skii, A. and Tkachenko, M., Topological groups and related structures, Springer Science and Business Media, 2008.
6. Bandyopadhyay, C. and Modak, S., A new topology via ψ-operator, Proc. Nat. Acad. Sci. India 76(A)(IV), 317-320, (2006).
7. Dontchev, J., Idealization of Ganster-Reilly decomposition theorems, arXiv:math/9901017v1 [math.GN], 5 Jan 1999.
8. Dontchev, J., Ganster, M. and Rose, D., Ideal resolvability, Topol. Appl. 93, 1-16, (1999).
9. 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).
10. Hamlett, T. R. and Jankovic, D., Ideals in topological spaces and the set operator , Bull. U. M. I. 7(4-B), 863{874, (1990).
11. Hashimoto, H., On the *-topology and its applications, Fundam. Math. 156, 5{10, (1976).
12. Jankovic, D. and Hamlett, T. R., New topologies from old via ideals, Amer. Math. Monthly 97(4), 295-310, (1990).
13. Jankovic, D. and Hamlett, T. R., Compatible extensions of ideals, Boll. U.M.I. 7(6-B), 453-465, (1992).
14. Keskin, A., Noiri, T. and Yuksel, S., fI -sets and decomposition of RIC-continuity, Acta Math. Hungar. 104, 307-313, (2004).
15. Khtun, K., Al-omari, A. and Modak, S., Compacti cation on *-topology, Poincare Journal of Analysis & Applications 10(2), 349-358, (2023).
16. Khatun, K. and Modak, S., Topologies on the Function Space Y^X with Topological Group, Submitted.
17. Kuratowski, K., Topology I, Warszawa, 1933.
18. Levine, N., Semi-open sets and semi-continuity in topological spaces, The American Mathematical Monthly, 70(1), 36-41, (1963).
19. 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).
20. Modak, S., Remarks on dense set, International Mathematical Forum, 6(44), 2153-2158, (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 Selim, Sk., Set operator and associated functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 70(1), 456-467, (2021).
24. Modak, S., Selim, Sk. and Islam, Md. M., Sets and functions in terms of local function, Al-Qadisiyah Journal of Pure Science 27(1), 91-102, (2022).
25. Munkress, J., Topology Second Edition, Pearson New International Edition, 2014.
26. Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca. 36(3), 297-312, (1986).
27. Newcomb, R. L., Topologies which are compact modulo an ideal, Ph.D. Dissertation, Univ. of Cal. at Santa Barbara (1967).
28. Tyagi, B. K. and Luthra, S., Open-point and bi-point open topologies on continuous functions between topological (spaces) groups, Mat. Vesnik 74(1), 56-70, (2022).
2. Al-omari, A. and Noiri, T., Local closure functions in ideal topological spaces, Novi Sad J. Math. 12(2), 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. Arhangel'skii, A. and Tkachenko, M., Topological groups and related structures, Springer Science and Business Media, 2008.
6. Bandyopadhyay, C. and Modak, S., A new topology via ψ-operator, Proc. Nat. Acad. Sci. India 76(A)(IV), 317-320, (2006).
7. Dontchev, J., Idealization of Ganster-Reilly decomposition theorems, arXiv:math/9901017v1 [math.GN], 5 Jan 1999.
8. Dontchev, J., Ganster, M. and Rose, D., Ideal resolvability, Topol. Appl. 93, 1-16, (1999).
9. 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).
10. Hamlett, T. R. and Jankovic, D., Ideals in topological spaces and the set operator , Bull. U. M. I. 7(4-B), 863{874, (1990).
11. Hashimoto, H., On the *-topology and its applications, Fundam. Math. 156, 5{10, (1976).
12. Jankovic, D. and Hamlett, T. R., New topologies from old via ideals, Amer. Math. Monthly 97(4), 295-310, (1990).
13. Jankovic, D. and Hamlett, T. R., Compatible extensions of ideals, Boll. U.M.I. 7(6-B), 453-465, (1992).
14. Keskin, A., Noiri, T. and Yuksel, S., fI -sets and decomposition of RIC-continuity, Acta Math. Hungar. 104, 307-313, (2004).
15. Khtun, K., Al-omari, A. and Modak, S., Compacti cation on *-topology, Poincare Journal of Analysis & Applications 10(2), 349-358, (2023).
16. Khatun, K. and Modak, S., Topologies on the Function Space Y^X with Topological Group, Submitted.
17. Kuratowski, K., Topology I, Warszawa, 1933.
18. Levine, N., Semi-open sets and semi-continuity in topological spaces, The American Mathematical Monthly, 70(1), 36-41, (1963).
19. 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).
20. Modak, S., Remarks on dense set, International Mathematical Forum, 6(44), 2153-2158, (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 Selim, Sk., Set operator and associated functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 70(1), 456-467, (2021).
24. Modak, S., Selim, Sk. and Islam, Md. M., Sets and functions in terms of local function, Al-Qadisiyah Journal of Pure Science 27(1), 91-102, (2022).
25. Munkress, J., Topology Second Edition, Pearson New International Edition, 2014.
26. Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca. 36(3), 297-312, (1986).
27. Newcomb, R. L., Topologies which are compact modulo an ideal, Ph.D. Dissertation, Univ. of Cal. at Santa Barbara (1967).
28. Tyagi, B. K. and Luthra, S., Open-point and bi-point open topologies on continuous functions between topological (spaces) groups, Mat. Vesnik 74(1), 56-70, (2022).
Publicado
2025-09-02
Edição
Seção
Artigos
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).
