A bitopological space $(X, \tau_i, \tau_j)$ is said to be a $(i, j)\gamma$ -$T_1$ space iff for each pair of distinct points $x$ and $y$ in $X$, there exists $ij$-$\gamma$-open sets $G$ and $H$ containing $x$ and $y$ respectively such that $y \notin G$ and $x \notin H$.
The space is called a $(i, j)\gamma$-$T_2$ space iff for each pair of distinct points $x$ and $y$, there exist disjoint $ij$-$\gamma$-open sets $G$ and $H$ in $X$ such that $x \in G, y \notin G$ and $y \in H, x \notin H$.
For more the definition of $ij$-$\gamma$-open set is given below:
A set $A$ is said to be a $ij$-$\gamma$-open set if intersection of $A$ with each $ij$-preopen sets gives a $ij$-preopen set.
A set $A$ is said to be a $ij$-preopen set if $A \subseteq \tau_i$-$int(\tau_j$-$cl(A))$.