International Journal of Mathematics Trends and Technology
Volume 68 | Issue 4 | Year 2022 | Article Id. IJMTT-V68I4P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I4P518
| Received | Revised | Accepted |
|---|---|---|
| 19 Mar 2022 | 24 Apr 2022 | 29 Apr 2022 |
The aim of this paper is to study nano compactness with respect to nano ideal, called nano I-compact space and discuss some of their properties. Some of the result in compact spaces have been generalized in terms of nano I-compact spaces.
[1] Bhuvaneswari, K. and Thanga Nachiyar, R., On nano generalized -closed sets in nano topological spaces”.
[2] Bhuvaneswari, K. and Mythili Gnanapriya, Nano generalized closed sets in nano topological spaces.
[3] Berri, M.P., Porter, J.R. and Stephenson Jr., R.M., A survey of minimal topological spaces, Proc. Kanpur Topological Conference, 1968, General Topology and its Relations to Modern Analysis and Algebra – III, Academic Press, New York, 1970.
[4] Bankston, P., The total negation of a topological property, Illinois J. Math., 23 (1979), 241−252.
[5] Hamlett, T.R. and Jankovic, D., Compactness with respect to an ideal, Bull. Un. Mat. Ital., B(7)(4) (1990), 849−861.
[6] Hamlett, T.R. and Rose, D., Local compactness with respect to an ideal, Kyung Pook Math. J., 32 (1992), 31−43.
[7] Hashimoto, H., On the topology and its applications, Fund. Math., 91 (1976), 5−10.
[8] Jankovic, D. and Hamlett, T.R., New topologies from old via ideals, Amen. Math. Monthly, 97 (1990), 295−310.
[9] Krishna Prakash, S., Ramesh, R. and Suresh, R., Nano compactness and nano connectedness in nano topological space, International Journal of Pure and Applied Mathematics, 119(13) (2018), 107−115.
[10] Kelly, J.T., General Topology, D. Van Nostrand Company Inc., Princeton, 1955.
[11] Kuratowski, Topology, Vol. I, Academic Press, New York, 1966.
[12] Lellis Thivagar and Carmel Richard, Note on nano topological spaces, Communicated.
[13] Lellis Thivagar and Carmel Richard, On nano continuity, Mathematical Theory and Modelling (2013), 34−37.
[14] Levin, N., Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19 (1970), 89−96.
[15] Mukherjee, M.N., Bishwambhar, R. and Sen, R., On extension of topological spaces in terms of ideals, Topology and its Appl. 154 (2017), 3267−3172.
[16] Njastad, O., Remarks on topologies defined by local properties, Det-Norske, Vidensk-abs-Academi, Arh. I. Mat. Naturv, Klasse, Ny Serie, (8) (1966), 1−16.
[17] Njastad, O., Classes of topologies defined by ideals, Matematisk, Institutt, Universitetet. I. Trondheim (preprint).
[18] Newcomb, R.L., Topologies which are compact modulo an ideal, Ph.D., Dissertation, Univ. of Cal. At Santa Barbara, 1967.
[19] Nasef, A.A. and Mahmoud, R.A., Some applications via fuzzy ideals, Chaos, Solitons and Fractals, 13 (2022), 825−831.
[20] Parimala, M. and Jafari, S., On some new notations in nano ideal topological spaces, Euresian Bulletin of Mathematics, 1(3) (2018), 85−93.
[21] Porter, J., On locally H-closed spaces, Proc. London Math. Soc., 20(3) (1970), 193−204.
[22] Samuels, P., A topology formed from a given topology and ideal, J. London Math. Soc., 10(2) (1975), 409−416.
[23] Steen, I.A. and Seeback Jr., J.A., Counter examples in topology, Holt, Rinehart and Winster, New York, 1970.
[24] Vaidyanathaswamy, R., The localization theory in set topology, Proc. Indian Acad. Sci. Math. Sci., 20 (1945), 51−61.
[25] Vaidyanathaswamy, R., Set Topology, Chelsea Publishing Company, New York, 1960
S. Gunavathy, R. Alagar, "Nano Compactness with Respect to Nano Ideal in Nano Topological Space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 4, pp. 111-115, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I4P518
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