Operators in terms of $*$ and $\psi$
DOI:
https://doi.org/10.5269/bspm.51598Abstract
Through this paper we consider three operators in terms of operators $*$ and $\psi$ in an ideal topological space. Many properties of these operators have been discussed. Characterizations of Hayashi-Samuel spaces are obtained as applications of the properties.
References
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2. Dontchev, J., Idealization of Ganster-Reilly decomposition theorems, arXIV:math. Gn/9901017v1 [math.GN], (1999).
3. Dontchev, J., Ganster, M., Rose, D., Ideal resolvability, Topology Appl. 93, 1-16, (1999). https://doi.org/10.1016/S0166-8641(97)00257-5
4. Hamlett, T. R., Jankovic, D., Ideals in topological spaces and the set operator ψ , Boll. Un. Mat.Ital. 7 (4-B), 863-874, (1990).
5. Hashimoto, H., On the *-topology and its applications, Fund. Math. 91, 5-10, (1976). https://doi.org/10.4064/fm-91-1-5-10
6. Hayashi, E., Topologies defined by local properties, Math. Ann. 156, 205-215, (1964). https://doi.org/10.1007/BF01363287
7. Jankovic, D., Hamlett, T. R., New topologies from old via ideals, Amer. Math. Monthly, 97, 295-310, (1990). https://doi.org/10.1080/00029890.1990.11995593
8. Kuratowski, K., Topology, Vol. I, New York, Academic Press, (1966).
9. Modak, S., Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 82 (3), 233-243, (2012). https://doi.org/10.1007/s40010-012-0039-3
10. Modak, S., Bandyopadhyay, C., A note on ψ-operator, Bull. Malays. Math. Sci. Soc. (2) 30(1), 43-48, (2007).
11. Newcomb, R. L., Topologies which are compact modulo an ideal, Ph. D. Dissertation, Univ. of Cal. at Santa Barbara, (1967).
12. Njastad, O., Remarks on topologies defined by local properties, Avh. Norske Vid. Akad. Oslo I(N.S), 8, 1-16, (1966).
13. Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca, 36 (3), 297-312, (1986).
14. Samuel, P., A topology formed from a given topology and ideal, J. London Math. Soc. 10, 409-416, (1975). https://doi.org/10.1112/jlms/s2-10.4.409
15. Selim, Sk., Noiri, T., Modak, S., Some set-operators on ideal topological spaces (submitted).
16. R. Vaidyanathswamy, The localization theory in set-topology, Proc. Indian Acad. Sci. 20, 51-61, (1945). https://doi.org/10.1007/BF03048958
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2022-12-22
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