?N-??g -Closed and open sets in grill nano topological spaces

Abstract

The initiator of nano topology was Lellis Thivagar \cite{8} and Choquet \cite{7} introduced grill topology in 1947. Nano topology was represented in terms of similarity and boundary region of a subset by using an equivalence relation on it. Lellis Thivagar developed the notion of nano closed set, nano interior and nano closure and also introduced the notion of nano semi closed and nano $\alpha$ closed sets. A. A. Azzam \cite{1} introduced grill nano generalized closed sets in grill nano topological space in 2016. Chandramathi and Sujithra \cite{3} introduced $\Re\omega g$-closed sets in grill topological spaces in 2019. In this paper, we initiate a new class of generalized closed set named as grill nano $\Re\omega g$-closed set ($\varsigma\mathfrak{N}-\Re\omega g$-closed) in the grill nano topological space.