Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 3, Issue 1, April 2019, Pages: 47-59

An introductory notes to ideal binanotopological spaces

I. Rajasekaran 1* and O. Nethaji2

1Department of Mathematics, Tirunelveli Dakshina Mara Nadar Sangam College, T. Kallikulam - 627 113, Tirunelveli District, Tamil Nadu, India.
2Research Scholar, Department of Mathematics, School of Mathematics, Madurai Kamaraj University, Madurai, Tamil Nadu, India.


In this paper, we made an attempt to unveil to notion of local functions, weak forms of n1,2 -open sets an ideal binanotopological spaces, (1, 2)* nano-Ig -closed sets, (1, 2)* nano *-g-closed sets and (1, 2)* nano - Ig-*-closed sets are introduced and their properties are discussed with suitable examples. They are characterized in the context of an ideal binanotopological space.


semi-nI -regular set, pre-nI -regular set and β -nI -regular set.


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1. K. Bhuvaneswari and H. Rasya Banu, On nano (1,2)* -generalized α-closed sets in nano bitopological space, International Journal of Science and Research, 5(4)(2016), 1292-1295.

2. K. Bhuvaneswari and R. Srividhya, On nano pre generalized closed sets in nano bitopological spaces, International Journal of Engineering Science and Computing, 6(3)(2016), 3084-3087.

3. J. Dontchev, M. Ganster, T. Noiri, Unified operations approach of generalized closed sets via topological ideals, Math. Japon. 49(1999) 395-401.

4. D. Jankovi’c and T. R. Hamlett, Compatible extensions of ideals, Boll. Un. Mat. Ital., 7(6-B)(1992), 453-465.

5. J. C. Kelly, Bitopological spaces, Proc. London Math. Soc., 13(1963),71-89.

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

7. M. Lellis Thivagar and Carmel Richard, On nano forms of weakly open sets, International Journal of Mathematics and Statistics Invention,1(1)(2013), 31-37.

8. N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(2)(1970), 89-96.

9. M. Navaneethakrishnan, J. Paulraj Joseph and D. Sivaraj, Ig -normal and Ig -regular spaces, Acta Math. Hungar. 125(2009), 327-340.

10. Nirmala Rebecca Paul, On generalised closed sets in nano bitopological spaces, Mathematical Sciences International Research Journal, 3(2)(2014), 538-541.

11. M. Parimala and S. Jafari, On some new notions in nano ideal topological spaces, International Balkan Journal of Mathematics(IBJM), 1(3)(2018), 85-92.

12. Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11(5)(1982), 341-356.

13. I. Rajasekaran and O. Nethaji, On (1,2)* nano b-open sets and (1,2)* nano β -open sets in binanotopological spaces, Communicated.

14. I. Rajasekaran and O. Nethaji, Simple forms of nano open sets in an ideal nano topological spaces, The Journal of New Theory, 24(2018), 35-43.

15. R. Vaidyanathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci., 20(1945), 51-61.

16. R. Vaidyanathaswamy, Set topology, Chelsea Publishing Company, New York, 1946.

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