ON Q-BITOPOLOGICAL SPACES

We study here $T_{0}$-$Q$-bitopological spaces and sober $Q$-bitopological spaces and their relationship with two particular Sierpinski objects in the category of $Q$-bitopological spaces. The epireflective hulls of both these Sierpinski objects in the category of $Q$-bitopological spaces turn out to be the category of $T_0$-$Q$-bitopological spaces. We show that only one of these Sierpinski objects is sober $Q$-bitopological space and its epireflective hull in the category of $T_0$-$Q$-bitopological spaces turns out to be the category of saturated $T_{0}$-$Q$-bitopological spaces.