Certain Investigations on Digital Plane

Abstract

We introduce the concept of $^\#g\hat{\alpha}$-closed sets in a topological space and characterize it using $^*g\alpha o$-kernel and $\tau^\alpha$-closure. Moreover, we investigate the properties of $^\#g\hat{\alpha}$-closed sets in digital plane. The family of all $^\#g\hat{\alpha}$-open sets of $(\mathbb{Z}^2, \kappa^2)$, forms an alternative topology of $\mathbb{Z}^2$. We prove that this plane $(\mathbb{Z}^2, ^\#g\hat{\alpha}O)$ is $T_{1/2}$ and $T_{3/4}$. It is well known that the digital plane $(\mathbb{Z}^2, \kappa^2)$ is not $T_{1/2}$, even if $(\mathbb{Z}, \kappa)$ is $T_{1/2}$.