Characterization of ultra separation axioms via $(1,2)\alpha$-kernel

In this paper, we introduce the concept of weakly-ultra-separation of two sets in a bitopological space using $(1,2)\alpha$-open sets. The $(1,2)\alpha$-closure and the $(1,2)\alpha$-kernel are defined in terms of this weakly-ultra-separation. We also investigate the properties of some weak separation axioms like ultra-$T_0$, ultra-$T_1$, and ultra-$R_0$.