Function Spaces under Various Operators
Abstract
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.
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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. 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).
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2025-09-02
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