On Nano πgα-Closed Sets

Yıl 2018, Sayı: 22, 66 - 72, 26.03.2018

İlangovan Rajasekaran Ochanan Nethaji

Öz

In this paper, we define and study the properties of a nano πgα-closed set which is
a weaker form of a nano πg-closed set but strong than a nano πgp-closed sets and we define a new
class of sets called nano πgα-closed sets and some of their properties.Thivagar et al. [4] introduced a nano topological space with respect to a subset X of an universe which is defined in terms of lower approximation and upper approximation and boundary region. The classical nano topological space is based on an equivalence relation on a set, but in some situation, equivalence relations are nor suitable for coping with granularity, instead the classical nano topology is extend to general binary relation based covering nano topological space Bhuvaneswari et al. [3] introduced and investigated nano g-closed sets in nano topological spaces. Recently, Parvathy and Bhuvaneswari the notions of nano gprclosed sets which are implied both that of nano rg-closed sets. In 2017, Rajasekaran et al. [7] introduced the notion of nano πgp-closed sets in nano topological spaces.

Anahtar Kelimeler

Nano π-closed set, nano πg-closed set, nano αg-closed set, nano πgp-closed set, nano gpr-closed set and nano πgα-closed set

Kaynakça

• [1] Adinatha C. Upadhya, On quasi nano p-normal spaces, International Journal of Recent Scientific Research, 8 (6) (2017), 17748-17751.
• [2] K. Bhuvaneshwari and K. Mythili Gnanapriya, Nano Generalizesd closed sets, International Journal of Scientific and Research Publications, 4 (5) (2014), 1-3.
• [3] K. Bhuvaneswari and K. M. Gnanapriya, On Nano Generalised Pre Closed Sets and Nano Pre Generalised Closed Sets in Nano Topological Spaces, International Journal of Innovative Research in Science, Engineering and Technology, 3 (10) (2014), 16825-16829.
• [4] M. L. Thivagar and C. Richard, On Nano forms of weakly open sets, International Journal of Mathematics and Statistics Invention, 1 (1) 2013, 31-37.
• [5] C. R. Parvathy and , S. Praveena, On Nano Generalized Pre Regular Closed Sets in Nano Topological Spaces, IOSR Journal of Mathematics (IOSR-JM), 13 (2) (2017), 56-60.
• [6] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11 (5) (1982), 341-356.
• [7] I. Rajasekaran and O. Nethaji, On some new subsets of nano topological spaces, Journal of New Theory, 16 (2017), 52-58.
• [8] I. Rajasekaran and O. Nethaji, On nano πgp-closed sets, Journal of New Theory, 19 (2017), 20-26.
• [9] R. T. Nachiyar and K. Bhuvaneswari, On Nano Generalized A-Closed Sets & Nano A- Generalized Closed Sets in Nano Topological Spaces, International Journal of Engineering Trends and Technology (IJETT), 6 (13) (2014), 257- 260.