Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces

İlangovan Rajasekaran; Ochanan Nethaji

Research Article

Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces

Year 2018, Issue: 24, 35 - 43, 14.08.2018

Abstract

In this paper, we introduce and study the new concepts called a-nI-open sets, semi-nI-open sets, pre-nI-open sets, b-nI-open sets and p-nI-open sets, which are simple forms of nano open sets in an ideal nano topological spaces. Also we characterize the relations between them and the related properties. And the independence of n-open sets and nI-open sets is established.

Keywords

n-open set, semi-nI-open set, ®-nI-open set, pre-nI-open set

References

[1] D. Jankovi'c and T. R. Hamlett, Compatible extensions of ideals, Boll. Un. Mat. Ital., 7 (6-B) (1992), 453-465.
[2] K. Kuratowski, Topology, Vol I. Academic Press (New York) 1966.
[3] M. L. Thivagar and C. Richard, On nano forms of weakly open sets, Interna- tional Journal of Mathematics and Statistics Invention, 1 (1) (2013), 31-37.
[4] M. Parimala, T. Noiri and S. Jafari, New types of nano topological spaces via nano ideals (to appear).
[5] 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.
[6] M. Parimala, C. Indirani and S. Jafari, On nano b-open sets in nano topological spaces, Jordan Journal of Mathematics and Statistics 9 (3) (2016), 173-184.
[7] Z. Pawlak, Rough sets, International journal of computer and Information Sci- ences, 11 (5) (1982), 341-356.
[8] A. Revathy and G. Ilango, On nano ¯-open sets, Int. Jr. of Engineering, Con- temporary Mathematics and Sciences, 1 (2) (2015), 1-6.
[9] R. Vaidyanathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci., 20 (1945), 51-61.
[10] R. Vaidyanathaswamy, Set topology, Chelsea Publishing Company, New York, 1946.

Year 2018, Issue: 24, 35 - 43, 14.08.2018

İlangovan Rajasekaran Ochanan Nethaji

Abstract

References

[1] D. Jankovi'c and T. R. Hamlett, Compatible extensions of ideals, Boll. Un. Mat. Ital., 7 (6-B) (1992), 453-465.
[2] K. Kuratowski, Topology, Vol I. Academic Press (New York) 1966.
[3] M. L. Thivagar and C. Richard, On nano forms of weakly open sets, Interna- tional Journal of Mathematics and Statistics Invention, 1 (1) (2013), 31-37.
[4] M. Parimala, T. Noiri and S. Jafari, New types of nano topological spaces via nano ideals (to appear).
[5] 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.
[6] M. Parimala, C. Indirani and S. Jafari, On nano b-open sets in nano topological spaces, Jordan Journal of Mathematics and Statistics 9 (3) (2016), 173-184.
[7] Z. Pawlak, Rough sets, International journal of computer and Information Sci- ences, 11 (5) (1982), 341-356.
[8] A. Revathy and G. Ilango, On nano ¯-open sets, Int. Jr. of Engineering, Con- temporary Mathematics and Sciences, 1 (2) (2015), 1-6.
[9] R. Vaidyanathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci., 20 (1945), 51-61.
[10] R. Vaidyanathaswamy, Set topology, Chelsea Publishing Company, New York, 1946.

There are 10 citations in total.

Details

Primary Language	English
Journal Section	Research Article
Authors	İlangovan Rajasekaran This is me Ochanan Nethaji This is me
Publication Date	August 14, 2018
Submission Date	April 29, 2018
Published in Issue	Year 2018 Issue: 24

Cite

APA	Rajasekaran, İ., & Nethaji, O. (2018). Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces. Journal of New Theory(24), 35-43.
AMA	Rajasekaran İ, Nethaji O. Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces. JNT. August 2018;(24):35-43.
Chicago	Rajasekaran, İlangovan, and Ochanan Nethaji. “Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces”. Journal of New Theory, no. 24 (August 2018): 35-43.
EndNote	Rajasekaran İ, Nethaji O (August 1, 2018) Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces. Journal of New Theory 24 35–43.
IEEE	İ. Rajasekaran and O. Nethaji, “Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces”, JNT, no. 24, pp. 35–43, August 2018.
ISNAD	Rajasekaran, İlangovan - Nethaji, Ochanan. “Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces”. Journal of New Theory 24 (August 2018), 35-43.
JAMA	Rajasekaran İ, Nethaji O. Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces. JNT. 2018;:35–43.
MLA	Rajasekaran, İlangovan and Ochanan Nethaji. “Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces”. Journal of New Theory, no. 24, 2018, pp. 35-43.
Vancouver	Rajasekaran İ, Nethaji O. Simple Forms of Nano Open Sets in an Ideal Nano Topological Spaces. JNT. 2018(24):35-43.