Operators in terms of $*$  and  $\psi$

Sk Selim; Takashi Noiri; Shyamapada Modak

doi:10.5269/bspm.51598

Sk Selim University of Gour Banga
Takashi Noiri
Shyamapada Modak University of Gour Banga

Résumé

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.

Téléchargements

Les données sur le téléchargement ne sont pas encore disponible.

Biographie de l'auteur

Shyamapada Modak, University of Gour Banga

Department of Mathematics

Associate Professor

Références

Al-Omari, A., Al-Saadi, H., A topology via ω-local functions in ideal spaces, Mathematics, 60 (83), 103-110, (2018). https://doi.org/10.24193/mathcluj.2018.2.01 DOI: https://doi.org/10.24193/mathcluj.2018.2.01

Dontchev, J., Idealization of Ganster-Reilly decomposition theorems, arXIV:math. Gn/9901017v1 [math.GN], (1999).

Dontchev, J., Ganster, M., Rose, D., Ideal resolvability, Topology Appl. 93, 1-16, (1999). https://doi.org/10.1016/S0166-8641(97)00257-5 DOI: https://doi.org/10.1016/S0166-8641(97)00257-5

Hamlett, T. R., Jankovic, D., Ideals in topological spaces and the set operator ψ , Boll. Un. Mat.Ital. 7 (4-B), 863-874, (1990).

Hashimoto, H., On the *-topology and its applications, Fund. Math. 91, 5-10, (1976). https://doi.org/10.4064/fm-91-1-5-10 DOI: https://doi.org/10.4064/fm-91-1-5-10

Hayashi, E., Topologies defined by local properties, Math. Ann. 156, 205-215, (1964). https://doi.org/10.1007/BF01363287 DOI: https://doi.org/10.1007/BF01363287

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 DOI: https://doi.org/10.1080/00029890.1990.11995593

Kuratowski, K., Topology, Vol. I, New York, Academic Press, (1966).

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 DOI: https://doi.org/10.1007/s40010-012-0039-3

Modak, S., Bandyopadhyay, C., A note on ψ-operator, Bull. Malays. Math. Sci. Soc. (2) 30(1), 43-48, (2007).

Newcomb, R. L., Topologies which are compact modulo an ideal, Ph. D. Dissertation, Univ. of Cal. at Santa Barbara, (1967).

Njastad, O., Remarks on topologies defined by local properties, Avh. Norske Vid. Akad. Oslo I(N.S), 8, 1-16, (1966).

Natkaniec, T., On I-continuity and I-semicontinuity points, Math. Slovaca, 36 (3), 297-312, (1986).

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 DOI: https://doi.org/10.1112/jlms/s2-10.4.409

Selim, Sk., Noiri, T., Modak, S., Some set-operators on ideal topological spaces (submitted).

R. Vaidyanathswamy, The localization theory in set-topology, Proc. Indian Acad. Sci. 20, 51-61, (1945). https://doi.org/10.1007/BF03048958 DOI: https://doi.org/10.1007/BF03048958